Physics 30 Electromagnetic Theory - Mrs. Unland - …mrsunland.weebly.com/.../13290043/wa_emag_principlesans.docx · Web viewpreviously separate fields of study in Physics were related

Physics 30 Electromagnetic Theory

Worksheet 1: Magnetism

1) What is believed to be the cause of all magnetic phenomena?

Moving charged particles produce a magnetic field. In ferromagnetic materials, it is the unpaired spins of electronsaligned in the same direction.

2) What is a magnetic domain?

A magnetic domain is an area in a ferromagnetic material in which the magnetic dipoles of atoms are all aligned in the same direction. The domain is said to be saturated with dipoles.

3) A magnet attracts one end of an iron bar and repels one end of a nickel bar. Further tests are made with these ends of the two bars. Explain why the following conclusions may or may not be justified.

a) The nickel bar is a magnet.Yes, repulsion is a sign that the nickel bar is a pole of like orientationb) The iron bar is definitely a magnetNo, the iron bar could simply be ferromagnetic and it wouldbe attractedc) The iron bar may be a magnetYes, the magnet could be acting on a pole of opposite orientation.d) The iron bar may be unmagnetizedYes, the iron bar could simply be ferromagnetic and it wouldbe attractede) The nickel bar will attract the iron barYes, since the nickel is a magnet, it should attract the iron bar whether it is a magnet or just ferromagnetic.

4) What is believed to be the major cause of the earth's magnetism?

It is thought that the liquid iron core of the earth is subjected to convection currents. The iron in this state is a charged plasma.

5) What type of magnetic pole exists in northern Canada?

The geographic north has a magnetic south pole.

6) What was significant of Oersted’s discovery that magnetic fields surround current carrying wires?

The discovery demonstrated that electricity and magnetism, two previously separate fields of study in Physics were related.

7) Who developed the left hand rules and formalized mathematical

equations describing the strength of magnetic fields?

Andre Ampere

8) What was Faraday’s contribution to the study of electromagnetism?

Faraday developed the motor principle in which electrical current can be converted into mechanical energy and the generatorprinciple in which mechanical energy can produce electricalpotential.

9) Who was Maxwell, and why was his contribution to electromagnetism so significant?

James Clerk Maxwell was the developer of the first comprehensivemathematical treatment of electromagnetism. He synthesized the work of Oersted, Faraday and his own conception of interacting electromagnetic fields to produce the four principles which form the classical wave conception of electromagnetism.

10) What was Langevin’s contribution to the study of magnetism?

Langevin is noted for his work on paramagnetism and diamagnetism and devised the modern interpretation of this phenomenon in terms of spins of electrons within atoms.

11) What two types of motion within the atom contribute largely toward the magnetic properties of atoms? Which is these ismore critical in explaining ferromagnetic properties?

1) The motion of electrons around the nucleus and 2) the motion of electrons spinning on their axis. The more important to ferromagnetic properties is the spin of electrons on their own axis.

12) a) What is magnetic flux? State the properties of a flux line.b) What is the definition of a magnetic field?

Magnetic flux (Greek letter Φ) is a measure of the magnetic field strength existing on a two dimensional surface, such as one side of a magnet. In textbook diagrams, magnetic flux is usually pictured as cluster of vectors attached to a geometrically abstract surface.

1) run from N to S outside the magnet 2) are closed curves (run south to north inside)3) flux lines do not cross 4) flux lines repel one another 5) concentration indicates the flux density(in Teslas) 6) follow the path of least resistance 7) tend to shorten

A magnetic field is the area of magnetic force around a substance

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They can be caused by electric charge, by electric fields that vary in time and by elementary particles that possess their own 'intrinsic' magnetic field, a relativistic effect which is usually modeled as a spin of the particle.

13) State three ways to demagnetize a magnet.

1) Dropping2) Heating3) Removing from a source of alternating current.

14) What happens to the domains of an non-magnetized ferromagnetic object when it is placed in a magnetic field?

The domains oriented in the same direction grow and the domainsoriented in different directions will shrink.

15) If each of two N poles is doubled in strength, and at the sametime the distance between them is made half as great, what change occurs in the force between them?

Using ratio techniques and the concept that in a manner analogous to gravitational and electric fields, the magnetic force would be 16x as great.

16) How large is the region of influence of a magnet?

The magnetic field theoretically extends to infinity.

17) Three identical bar magnets are placed so that one pole of each lies on the circumference of a circle of radius 10 cm. The magnets are oriented as shown in the diagram below.

State the approximate direction in which the north end of a small magnetic compass needle would point, if its pivot coincided with the center of the circle. Explain your answer.

like poles repel and unlike poles attract. The vector sum of the repulsions and attractions of the north pole of the compass is shown above.

18) Name two elements other than iron which are strongly attracted by a magnet

Two other ferromagnetic elements are nickel and cobalt.

19) What are the advantages of making a magnetic in a horseshoe shape?

The horseshoe shape decreases the distance between the poles of the magnet and therefore concentrates the magnetic flux linesbetween the poles just on the basis of its shape.

20. Define each of the following: a) declination b) dip c) permeability d) retentivity e) domain.

a) The angle between the magnetic pole and the geographicnorth pole.b) The angle between the horizontal and the magnetic field inclination to the ground.c) The rate of magnetization of a material in response to a magnetic field.d) The degree to which a substance retains its magnetism after a magnetizing field is removed.

Worksheet 2: Magnetic Fields for Current Carrying Wires

1) Calculate the magnetic field 9.0 cm from a long straight conductor carrying a current of 3.0 A. (6.7 x 10-6 T)

2) Calculate the current in a long straight conductor if it produces a magnetic field of 2.6 x 10-5 T at a distance of 25 cm from the conductor. (33 A)

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3) A 25.0 cm solenoid has 1800 loops and a length of25.02 cm. Calculate the magnetic field in the air core of the solenoid when a current of 1.25 A is flowing. (1.13 x 10-2 T)

4) A circular coil with 190 loops of wire has a length of3.40 cm. If the magnetic field at the center of this coil is6.2 x 10-3 T, what is the current flowing through the coil?(0.88 A)

5) An air core solenoid is 25 cm long and carries a currentof 0.72 A. If the magnetic field in the core is 2.1 x 10-3 T, how many turns does this solenoid have? (580)

6) Two long fixed parallel wires are 7.2 cm apart and carry currents of 25 A and 15 A in the same direction. What is the magnitude of the magnetic field midway between the two wires? (5.6 x 10-5 T)

7) The earth's magnetic flux density is approximately 3.0 x 10-5 TAt what distance from a long straight vertical wire carrying a current of 8.0 A does the flux balance the earth's field? (5.3 cm)

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8) A beam of 1.25 x 1010 e-/s leaves an accelerator with a speed of 2.0 x 106 m/s. Calculate the magnetic flux density 4.0 cm from the beam. (1.0 x 10-14 T)

9) What is the magnetic field strength at the center of a loop of wire: a) 15.0 cm in diameter which is carrying a current of 17.5 A? (1.47 x 10-4 T)b) the same as in a, but with 300 loops/m.(4.40 x 10-2 T)

10) A current carrying wire has a magnetic field of 3.2 x 10-5 T at a distance of 3.0 cm from the wire. If the current is tripled and the distance from the wire is reduced to 1.0 cm, what will the magnetic field strength be at this new location? (2.88 x 10-4 T)

11) Two long fixed parallel wires are 8.00 cm apart and carry currents of 15 A and 35 A in opposite directions. What is the magnitude of the magnetic field midway between the two wires? (2.5 x 10-4 T)

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Worksheet 3: Motor Principle

1) A copper wire (L = 0.222 m) carries conventional current of 0.960 A north through magnetic field (= 7.50 x 10-4 T) that is directed vertically upward. What is the magnitude and direction of the magnetic force acting on the wire? (1.60 x 10-4 N East)

2) A solenoid lies in a horizontal plane with a current balance, WXYZ, balanced horizontally in the solenoid core at points Z and W as shown in the diagram. Sides WX and ZY of the current balance conductor are 7.10 cm. Side YX is 1.90 cm. A current of 6.00 A flows through the conductor on the current balance. If a mass of 1.76 x 10-2 kg is necessary to balance the current balance, what is the magnetic field strength in the solenoid? (1.51T)

3) A wire in the armature of an electric motor is 2.50 x 10-1 m long and is perpendicular to a magnetic field of 5.00 x 10-1 T. Calculate the magnetic force on the wire when it carries a current of 3.60 A. (4.50 x 10-1 N)

4) A current balance is used to determine the magnetic field intensity in the core of a solenoid. The current balance and the solenoid are described in the diagram. If the current balance is balanced with a 2.3 x 10-5 kg mass, what is the magnetic field strength in the solenoid core? (3.3 x 10-2 T)

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5) From the diagram below:

a) What kind of pole is at X?b) Connect the ends of one dry cell to the ends of the coil to produce the pole indicated in the diagram.c) If a copper core were substituted for the iron, what would happen to the strength of the pole at X?

a) X must be a south pole to attract the north of the compass.b) To produce a south pole at X, the current would have to comefrom the back to the front. The wire at the X end should be connected to the negative terminal of a battery, and the wire onthe other end should be connected to the positive terminal.c) Copper is not ferromagnetic. The iron bar down the centerproduces a stronger magnetic because the domains align in the direction of the magnetic field caused by the current. Copper will therefore not produce as strong a magnetic field.

6) A bare current-carrying wire runs across a lecture table. Describe at least two ways you could find the direction of the current.

1) Use a compass – the compass will align in the direction of the magnetic field when you place the compass at different points around the wire. The pole from the wire can be used to find the direction of the current using the left hand rule for current carrying wires.2) Bring a strong magnet close to the wire and tangent to an imaginary circle around the wire. When the magnet repels the wire, you will know that the two magnets are showing like poles. The pole from the wire can be used to find the direction of the current using the left hand rule for current carrying wires.

7) An electron current-carrying wire is placed between the poles of a magnet as shown at right. What is the direction of the force on the wire?

(out of the page towards you)

8) A rectangular loop is suspended by a spring scale between magnetic poles. The loop is 0.060 m wide by 0.120 m high.

Current in loop (A) Total Force on Spring

1.00 1.50322.00 1.50633.00 1.50944.00 1.51285.00 1.51596.00 1.5225

a) What is the weight, in Newtons, of the loop? b) What is the slope of the best fit line and what does it represent? c) What is the magnitude of the magnetic field between the bar magnets? (1.50 N, 3.68 x 10-3 N/A increase in Fmag per ampere of current,

(6.13 x 10-2 T)

L1= Current (A)L2= Total Force (N)

Note that in this case, the net force continues to get larger and larger as the current increases, indicating that the magneticforce in in the same direction as the gravitational force.

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LinReg(ax+b) L1,L2,Y1

a = 3.68 x 10-3 N/Ab = 1.50 Nr2 = 0.9770 …

min max scl

Window x[ 0.5 6.5 0.5 ] y[1.4999… 12.5257 … 0.005]

a) The weight of the loop is the Force when the current is zero,or the y intercept of the graph = 1.50 N

b) The slope of the graph is the Force each additional amp of current exerts on the bar. From the equation Fmag = IL it willalso represent the magnetic field times the length of wire in the magnetic field. Slope = 3.68 x 10-3 N/A

c) Since slope = Fmag /I = L slope/L =

= 3.677 … x 10-3/0.060 = 6.13 x 10-2 T

9) An experiment is carried out to investigate the relationship between the magnetic force F on a current-carrying wire in a uniform magnetic field B and the current I in the wire. The wire is placed in the plane of the page, as shown in the diagram below. The direction of the magnetic field is perpendicular to the plane of the page and directed into the page.

(i) On the diagram above, draw a vector to indicate the direction of the magnetic force on the wire when the current I is in the direction shown.

LHR thumb = current , fingers = magnetic field, palm = magnetic force

(ii) The current in the wire is decreased and the magnetic force on the wire is measured.

(1) State the responding variable in this experiment.

The responding variable in this case would be the Fmag

(2) Sketch a graph of the relationship between the two variables.

(iii) Calculate the magnitude of the force per unit length that acts on the wire if the current in the wire is 0.8 A. The magnitude of the magnetic field B is 1.2 × 10-4 T.

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10) Explain, with reference to the diagram of a moving-coil loudspeaker below, how the loudspeaker cone is set vibrating by an oscillating current flowing through the voice coil.

When the current goes into the page on the top coil, it will come out of the page on the bottom coil and vice versa. Using the left hand rule for the motor effect, the top and bottom will both pull in on the speaker cone when the current is as described. When the current reverses, the two interactions will both push the speaker cone out. This will produce sound waves of the same frequency as the current reversals in the coil.

11) Two long parallel wires carry currents of 5.0 A and7.5 A in opposite directions. If the force per meter on each wire is 5.3 x 10-5 N, how far apart are the wires? (0.14 m)

12) When a steady electric current of 10.0 A flows through the circuit shown in the diagram, the parallel wires X and Y attract each other with force of 5.00 x 10-5 N.

If X and Y have equal resistance, calculate the force they would exert on each other if the total current were increased to 20.0 A. (2.00 x 10-4 N)

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13) Two straight, parallel wires 8.0 m long and 0.50 m apart carry currents of 20 A in opposite directions.

a) What is the magnetic flux density at a point P midway between the wires? (3.2 x 10-5 T)

b) What is the magnitude of the force exerted on each wire? (2.6 x 10-3 N)

c) If the currents are in the same direction, what is the magnetic flux density at P? (0 T)

If the currents are in opposite directions, then the magnetic fields between the two wires will be going in opposite directions, andat the midpoint would be equal strengths. Hence the fields wouldsum to zero.

14) Two parallel wires are each 1.0 m long and 1.0 cm apart. If one of the wires carries a current of 10 A and the magnetic force between them is 1.0 x 10-4 N, what is the current in the second wire? (0.50 A)

15) The diagram shows an armature loop located between the poles of a permanent magnet.

In a sentence, describe the direction of the rotation of the armatureloop according to the polarity of the armature, the permanent magnets, and when viewed in the direction of the arrow.

The electric current would flow upward in the wire on the right and downward in the wire on the left.

LHR fingers = magnetic field thumb = electric current palm = motor force.

The left hand rule shows that the wire on the right will be pushed out and the wire on the left will be pushed in by the motor force. Viewed from below, the loop would turn counterclockwise.

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16) i) The diagram shows a coil ABCD of wire carrying a clockwise electric current I in a magnetic field directed to the right. In the space below, give the direction of the force acting on eachside of the coil:

AB = no force as the magnetic field of the top wire is perpendicular to the field magnet, so they do not interact.BC = using LHR, the motor force on BC will be into the page.CD= no force as the magnetic field of the top wire is perpendicular to the field magnet, so they do not interact.DA = using LHR, the motor force on DA will be out of the page.

ii) The diagram shows the same coil in a magnetic field directed into the page. On the diagram, at

right, show the direction of the forces acting on each side

of the coil.

Top wire = by left hand rule, will be pushed to the bottom of the page but this will not cause turning around the axis.Left side wire = by left hand rule will be pushed to the right side of the page, but this will not cause turning around the axis.Bottom wire = by left hand rule, will be pushed to the top of the page but this will not cause turning around the axis.Right side wire = by left hand rule will be pushed to the left side of the page, but this will not cause turning around the axis.

(iii) If the coil is initially stationary, will the magnetic forces in the diagram, at left above, cause it to move?

Yes, by the left hand rule for motor effect, the right wire will be pushed into the page, and the left wire will be pushed out of the

page, causing turning around the central axis.

(iv) A simple DC motor is constructed as shown in the diagram above. A coil is free to rotate about the axis of rotation in a magnetic field directed to the right in the diagram.

Label the diagram showing:

• The commutator.• The brushes.• The position of the north and south poles of a magnet which would produce the field shown.• The direction in which the coil will commence to rotate if it is initially stationary. (counterclockwise)

17) A small motor has a rotating loop consisting of 300 turns of wire in a rectangle whose ends are 6.00 cm and whose sides are 12.0 cm. The armature draws 4.00 A of current while the long sides of the loop are across a field whose flux density is

0.120 T. What is the torque on the armature? (1.04 N.m)

18) A rectangular coil ABCD of dimensions 8·0 cm by 4·0 cmis made up of 250 turns of wire. It is placed in a uniform magnetic field with a flux density of 0·50 T. It is free to rotate about an axis, PQ, as shown in the diagrams below. A current of 9·0 mA flows through the coil.

a) Draw a diagram, from above, showing the angle of the coil in the field when the torque is maximal.

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b) The coil is then rotated 180° around axis PQ from the position of maximum torque. Compare the torque in this position with that described in part (a).

The torque will again be maximal.

c) What is the magnitude of the maximum torque?

d) What is the magnitude of the force on side BC of the coil when the torque is maximum? ( 4.5 x 10-2 N)

19) Two large bar magnets and a vertical coil are shown in the diagram. The coil, ABCD, is able to rotate about a vertical axle,XY, through its centre. The coil consists of 140 turns of wire. Current can flow into and out of the coil along wires attached to the upper end of the axle. The coil is 22 cm high and 13 cm wideThe magnetic flux density between the poles of the magnets is 0.80 T.

a) Before the current in the coil is turned on, what is the fluxthrough the coil when the plane of the coil is parallel to the field?

b) When a current of 3.0 A flows through the coil, calculate the

magnitude of the force on side AB of the coil. (74 N)

c) Calculate the torque on the coil when the plane of the coil is at an angle of 35° to the magnetic flux as shown below. (The view shown is from above – Hint: find where the torque would be maximal)

d) If the magnets and the coil described above are used as the basis for an electric motor, what should be added to allow the coil to keep rotating in the same direction?

Split ring commutator

20) If you wanted to produce the world’s strongest electric motor,explain how you would construct it.

The commutator should be large with many wraps of wire, avery strong magnetic field and a large electric current.

21). A coil consists of ten turns of insulated copper wire. It is placed between the poles of magnets as shown in the diagram. These magnets may be assumed to create a uniform magnetic field of flux density 0·15 T. A current of 2·0 A is passed through the coil in the direction shown.

a) Calculate the torque that acts on the coil when it is in the

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position shown in the diagram. (4.5 x 10-3 Nm)

b) With electric current going into the left hand of the coil, in what direction will the coil start to turn as seen from position Z? (clockwise)c) A device is placed at Z to allow current to be supplied to the coil so that the coil rotates continuously.i) Name the device.ii) Explain how it works.

22) The diagram shows a plan (view from above) of a simple electric motor. ABDC represents a wire coil which is able to rotate about the axis of rotation shown.

(a) On this diagram show(i) The magnetic field between the poles of the magnet;(ii) The direction of the electric current flowing in the side AB of the coil.

(b) If the magnetic field has strength 1.0 T and a current of 5.0 A flows through each wire in the coil, what is the force (magnitude and direction) on a single wire in side AB of the coil? The sides of the coil (AB and CD) have length 0.20 m each. (c) State why the arrangement as shown could not work as a practical motor and describe briefly the modifications which must be made in order that the motor can turn freely.

23) Calculate the magnitude and the direction of the magnetic force on an electron travelling north at a speed of 3.52 x 105 m/s through a vertically upward magnetic field of 2.80 x 10-1 T. (1.58 x 10-14 N West)

24) Calculate the magnitude and the direction of the magnetic force on an alpha particle travelling south at a speed of 7.40 x 104 m/s through a vertically upward magnetic field of 5.50 T.(1.30 x 10-13 N West)

25) Calculate the magnitude and the direction of the magnetic field that produces a magnetic force of 1.70 x 10-14 N East on a proton that is travelling 1.90 x 104 m/s North through the magnetic field. (5.59 T up)

26) An electron experiences an upward force of7.1 x 10-14 N when it is travelling 2.7 x 105 m/s souththrough a magnetic field. What is the magnitude anddirection of the magnetic field? (1.6 T West)

27) Calculate the magnitude and the direction of the magnetic force on an alpha particle travelling upward at a speed of 2.11 x 105 m/s through a magnetic field that is directed down. (0)

28) An electron is accelerated from rest by a potential difference of 1.70 x 103 V, and then enters a magnetic fieldof 2.50 x 10-1 T moving perpendicular to it. What is the magnitude of the magnetic force acting on the electron?(9.77 x 10-13 N)

29) An electron is accelerated by a potential difference and then travels perpendicular through a magnetic field of7.20 x 10-1 T where it experiences a magnetic force of4.1 x 10-13 N. Assuming this electron starts from rest, through what potential difference is the electron accelerated? (3.6 x 101 V)

30) Calculate the downward acceleration on an electron that is travelling horizontally at a speed of 6.20 x 105 m/s perpendicular to a horizontal magnetic field of2.30 x 10-1 T. (2.50 x 1016 m/s2)

31) A proton travelling vertically at a speed of 2.10 x 105 m/s through a horizontal magnetic field experiences a magnetic force of 9.50 x 10-14 N. What is the magnitude of the magnetic field? (2.83T)

32) Calculate the downward acceleration on a proton that is moving horizontally at a speed of 7.50 x 105 m/s perpendicular to a horizontal magnetic field of 2.70 x 10-1 T. (1.94 x 1013 m/s2)

33) Ions travelling at a velocity of 3.50 x 107 m/s pass undeflected through the velocity selector in a mass spectrometer. If the magnetic field strength in the velocity selector is 0.500 T, what is the electric field strength in the velocity selector? (1.75 x 107 N/C)

34) A velocity selector is composed of a uniform magnetic field ( = 4.00 x 10-2 T) and a uniform electric field

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perpendicular to each other. If the electric field is produced by using parallel plates that are 1.50 cm apart, what is the potential difference between the plates that will permit singly charged ions of speed 4.20 x 106 m/s to pass undeflected through the selector? (2.52 x 103 V)

35) Singly charged ions pass undeflected through the velocity selector of a mass spectrometer. This velocity selector has a magnetic field ( = 2.50 x 10-1 T) and an electric field (|E| = 7.00 x 103 V/m) perpendicular to each other. These ions now enter the separation region where the magnetic field is the same as in the velocity selector. If the radius of the deflected ions is 8.12 x 10-3 m, what is the mass of each ion? (1.16 x 10-26 kg)

36) A singly charged 7-Li ion (mass = 1.16 x 10-26 kg) is accelerated from rest through a potential difference of 4.00 x 104 V. This ion then enters a magnetic field ( = 0.700 T) perpendicular to it. What is the radius of the deflected ion? (1.09 x 10-1 m)

37) An ion source contains two isotopes of magnesium (24-Mg, 25-Mg). These ions travel undeflected through the velocity selector ( = 0.850 T, |E| = 4.60 x 105 V/m) of a mass spectrometer. If both isotopes are singly charged, how far apart are the lines on the ion detector? (Assume the magnetic field strength in the ion separator is 0.250 T.) (0.045 m)

38) A singly charged carbon ion travels in a circular path (R = 11.3 cm) through the ion separation region of a mass spectrometer. If the velocity selector is composed of an electric field (|E| = 7.50 x 104 N/C) and a magnetic field(= 0.300 T) perpendicular to each other, what is the mass number of the carbon isotope? (Assume that the ion separation region also has a magnetic field of 0.300 T) (13)

39) In a mass spectrometer, a velocity selector allows singly charged carbon-14 ions with a velocity of 1.00 x 106 m/s to travel undeflected through the selector. If these ions enter the ion separation region ( = 0.900 T), what is the radius of the ions' path? (0.163 m)

40) In a mass spectrometer it is found that the radius of the path for singly charged 20-Ne ions is 15.1 cm in the ion separation region. What would be the radius of the path for singly charged 16-0 ions, assuming identical velocities in the same mass spectrometer? (12.1 cm)

41) A beam of Pb2+ ions (mass = 3.44 x 10-25 kg) travel through the velocity selector of a mass spectrometer at a velocity of 5.00 x 104 m/s. What magnetic field strength is required in the ion separation region to cause these ions to travel in a circular path with a radius of 19.6 cm?(0.274 T)

42) Doubly charged neon atoms are accelerated from rest through a potential difference of 2.00 x 103 V. They then enter a perpendicular magnetic field ( = 0.200 T) and move in acircular path with a radius of 10.2 cm. What is the mass of the neon ion? (3.33 x 10-26 kg)

43) A student using a mass spectrometer with a constant magnetic field studied the relationship between the radius of the circular path of a number of singly charged isotopes and their momentum. The following data was determined:(a = 9.0 x 1018 m/Ns b = -1.6 x 10-3 m = 0.69 T)Momentum Radius(x 10-20 kg•m/s) (x 10-1 m)

0.83 0.74 1.4 1.21.7 1.52.6 2.43.2 2.83.7 3.3

a) Draw a graph plotting radius as a function of momentumb) Using a suitable averaging technique, determine the magnetic field used in the spectrometer. (0.69 ± 0.01 T)

44) What are the Van Allen belts and why do they ‘lift’ at night?

45) The Earth's magnetic field in space is stronger near the poles than over the equator. At what location would the circular paths followed by the charged particles around the magnetic field lines have larger radii? Explain.

46) The Earth is under continual bombardment from energetic, charged particles. The magnetic field of the Earth influences the path of these particles. Draw a diagram and explain the different paths these particles take as they approach the Earth’s magnetic field at the equator or towards the poles.

47) A beam of electrons traveling at 1.8 x 108 m/s is directed towards a 0.014 T magnetic field as shown in the diagram at left below.

a) Which of the diagrams, at right above, illustrates the path of the electron beam once in the magnetic field? (Circle one.)b) What is the radius of the path of the electron beam while in the magnetic field? (0.073 m)

48) During periods in which the sun is particularly active (as it was in the year 2001), explosions on the sun's surface can

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result in high-energy protons and electrons leaving the sun and striking the earth some time later

(a) (i) If the protons have speed 6.0 x 107 m/s and the earth is 1.5 x 1011 m from the sun, how long does it take for the protons to reach the earth? (2.5 x 103 s) (ii) What would be the radius of the circular path taken by these protons if they enter a region in which the earth's magnetic field has a value of 5.0 x 10-8 T, and the protons travel perpendicular to the field lines? (1.3 x 107 m)

(b) The charged particles are deflected by the earth's magneticfield towards the earth's poles where they excite oxygen atoms (among others) in the upper atmosphere. The oxygen atoms then emit red and green light that can be seen in the sky as the 'auroras'. The diagram shows the relevant energy levels within the oxygen atom and the electronic transition responsible for the red light. What is the wavelength of the red light? ( Use E = hc/where h is Planck’s constant) (6.25 x 10-7 m)

(c) The ions bombarding the atmosphere can set up electric currents in the earth's upper atmosphere (the 'ionosphere'). Assume that the current is very thin as if flowing in a wire.

(i) The current is 100 km above the earth's surface and has value 5.00 x 106A. At a point on the earth's surface directly beneath the current, what is the magnitude of the magnetic field strength produced by this current? (1.00 x 10-5 T) (ii) If the current runs from south to north, what is the direction of the magnetic field in part (i)? (East)

Worksheet 4: Electromagnetic Induction (Ohms law V = IR where R is resistance in ohms)

1) A conducting rod 0.35 m long moves perpendicular to a magnetic field (= 0.75 T) at a speed of 1.5 m/s. Calculate the induced voltage in the rod. (0.39 V)

2) The line MN in the diagram shown below represents a straight conductor 0.20 m long which is perpendicular to a magnetic field of induction 5.0 T. Calculate the magnitude of the E.M.F., which is generated when the conductor moves vertically into the paper,so that it cuts through the field with a constant velocity into the

paper, of 10 m/s. (10 V)

3) Part of a closed circuit consists of a straight wire 1.5 m long moving at a speed of 2.0 m/s perpendicular to a magnetic field of 10 000 G (104 Gauss = 1T). What is the EMF induced in the circuit? (3.0 V)

4) A wire 50 cm long is at rest along the +x axis. A large magnet generating a uniform field directed along the +y direction, of magnitude 0.2 T, is moved in the +z direction with a speed of 30 m/s. Find the magnitude and direction of the EMF induced in the wire. (3 V in the +x direction)

5) A metal bar 8.0 cm long is dropped crosswise through a magnetic field whose flux density is 1.5 x 10-2 T. a) What is the EMF between its ends if it passes through the field at a velocity of 4.0 m/s? (4.8 x 10-3 V)b) How fast must a 30. cm bar drop through the field in the

prior problem to produce an EMF of 12 V? (2.7 x 103 m/s)

6) A wire, 20.0 m long, moves at 4.0 m/s perpendicularly through a 0.50 T magnetic field. What EMF is induced in the wire? (40 V)

7) In the figure below, assume that L is 0.10 m long and B is 5.0 T.

a) Calculate the induced EMF when L is moving at 10.0 cm/s to the left (0.050 V)b) State three ways of increasing the EMF generated in a).

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c) If the induced current is 0.500 A, what force is needed to move L at 10.0 cm/s (0.25 N)d) Where does the energy come from to maintain this current?e) If the electrical resistance of the rectangular circuit is increased, how would the power required to maintain the same current change? f) In which direction do electrons move in wire L of the rectangular circuit of the diagram when L is moved to the right?

8) The conducting rod in the diagram below is 22.0 cm long, and is moving at a speed of 1.25 m/s perpendicular to a 0.150 T magnetic field. If the resistance in the circuit is 2.25 , what is the magnitude and direction of the current (electron flow) through the circuit? (1.83 x 10-2 A clockwise)

9) The conducting rod in the diagram below is 15 cm long, and is moving at a speed of 0.95 m/s perpendicular to the magnetic field.

If the resistance in the circuit is 1.5 , and a current of 5.6 x 10-2 A is induced in the circuit,a) what is the magnitude of the magnetic field? (0.59 T)b) what is the direction of the induced current (electronflow)? (clockwise)

10) The conducting rod in the diagram below is 30.0 cm long perpendicular to a 0.950 T magnetic field. .If the resistance in the circuit is 3.25 what force is required to move the rod at a constant 1.50 m/s? (3.75 x 10.-2 N)

11) A plane with a wing span of 6.25 m is flying horizontally at a speed of 95.0 m/s. If the vertical component of the earth's

magnetic field is 4.70 x 10-6 T, what is the induced voltage between the tips of the wings? (2.79 x 10-3 V)

12) A rectangular coil of wire containing 5 loops is movedat a speed of 2.7 m/s perpendicular to a 1.1 T magnetic field as shown below. If the length of the side of the coil moving perpendicular to the field is 0.18 m, and the resistance in the circuit is 3.5 ,a) what is the induced current? (0.76 A)b) what is the direction of the current (electron flow)?(counterclockwise)

Worksheet 5: Lens’s Law

1) Explain how you can determine the direction of an induced E.M.F. (as viewed from above) with the use of Lenz's law. Assume that the north pole of a magnet has been inserted into the coil shown.

2) Many sensitive chemical balances are fitted with a magnetic damper. Instead of the pointer swinging almost endlessly, it comes to rest quickly. (See diagram) The damper is merely a strip of aluminum attached to the pointer, which passes between the magnet the jaws of a strong permanent magnet when the pointer swings. Explain why this simple arrangement reduces the speed of the pointer's movements.

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3) In the diagram below, coil P is set oscillating so that it passes up and down over the end of a magnet. Coil Q begins to move also. Explain why this happens.

4) When a bar magnet moves toward the copper ring electrons flow as shown below

What kind of pole is X? Explain.b) When the magnet is alternately moved away from and toward the ring at a given rate without touching it, the ring will begin to move back and forth about the suspended strings as if it were a pendulum. Explain.c) If instead of copper the ring is made of nichrome (the mass remaining the same - nichrome is the resistance wire found in toasters) the ring will move back and forth with smaller

amplitude. Explain

5) The arrows show the direction of the winding not the current direction

Two coils, A and B are connected as shown in the diagram. A magnet is pushed into coil A. Describe the subsequent motionof the magnet which is suspended by a light spring in coil B.

6) Electron flow is increasing in coil A in the figure below. In which direction will a current be induced in coil B? If the current were decreasing in A, what would be the direction?

7) The magnet is pushed completely through the loop of the figure below. What changes take place both in the direction and magnitude of the induced current in the loop?

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8) (i) What is does Lenz's Law state about the direction of an induced current?(ii) A bar magnet moves downwards into a conducting coil as shown in the diagram causing an induced current to flow in the coil. On the diagram sketch:

• The lines of magnetic force around the bar magnet.• The lines of magnetic force produced by the induced current in the coil.• The direction of the induced current in the coil and external circuit.

Be sure to label clearly your additions to the diagram.

(iii) What would happen to the direction and magnitude of the induced current as the bar magnet fell through the coil and emerged from the bottom of the coil? Explain your answer. A reasonable sketch graph of current against time should be included.

Worksheet 6: Generators and Motors

1) What is the difference between a generator and a motor?

2) The diagram shows a simplified electric motor circuit.

On the diagram and using arrows, show the direction of the current in the coils and each side of the armature loop as well as the direction that each side of the armature loop is moving. 3) An electric motor in a hair drier is running at normal speed and, thus, is drawing a relatively small current. What happens to the current drawn by the motor if the shaft is prevented from turning, so the back EMF is suddenly reduced to zero? Remembering that the wire in the coil of the motor has some resistance, what happens to the temperature of the coil? Justify your answers.

4) The diagram below shows in outline an AC electric generator. When a force (due to a jet of high velocity water or high velocity steam for example) is applied to the turbine, both the turbine and coil spin between the poles of a strong magnet in an anticlockwise direction.

(a) Explain why an electromotive force is generated in a conducting wire which moves through a magnetic field.

(b) On the diagram above indicate the direction of the magnetic field line between the magnets; and the direction of the induced EMF (if any) in each section of the rotating coil (for the instant of time shown on the diagram).

(c) Water strikes the turbine, turning the generator and causing a current to flow in the external circuit. Explain how the principal of conservation of energy applies to this series of events.

5 )The diagram shows a simple electric generator in which acoil of wire rotates inside a strong magnetic field.)

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(i) With labeled arrows, indicate the following on the diagram:- the direction of the magnetic field in the region of the coil- the direction of the (conventional) current flowing in theexternal circuit. (ii) Is the current produced by this generator alternating or direct?Explain your answer. (iii) At the position of the coil shown in the diagram, is the valueof the current at a maximum or is it zero? Explain. (iv) A direct current electric motor also contains a wire coil, which rotates in a magnetic field. Explain how you would modify theabove arrangement so as to obtain such a DC motor. Draw adiagram to illustrate your answer in the space opposite.

Worksheet 7: Maxwell and Hertz

1) List four principles that Maxwell used to formulate his theory of electromagnetic radiation.

2) Suppose that the electric field of an electromagnetic wave decreases in magnitude. Does the magnetic field increase, decrease, or remain the same? Account for your answer.

3) What are the characteristics of electromagnetic waves? Do they behave differently than other waves? Explain.

4) Television antennas normally have the receiver antennas in a vertical position. From that, what can you deduce about the directions of the electric fields in television signals?

5) Why must an alternating current dipole be used to generate electromagnetic waves? What would happen if a direct current source were used?

6) The diagram shows a representation of the apparatus used by Hertz to detect electromagnetic waves.

Describe how you might determine:a) whether the waves are polarized. b) the wavelength of the wavesc) the velocity of the waves

7) What are the causes of each of the following type of electromagnetic wave:

i) radioii) microwaveiii) infrared lightiv) visible lightiv) x-raysv) gamma rays

8) What happens to each of the following as the wavelength of electromagnetic radiation gets shorter:

i) penetrating powerii) energyiii) wavelengthiv) frequency

9) What wavelengths of EMR are called ionizing radiation? What does this term mean?

10) What types of EMR are capable of passing through the earth’s atmosphere from outer space?

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