AP Physics 11: Magnetism Name __________________________A. Magnetic Properties

1. magnetic Field, Ba. circular field around a straight current wire

into the page out of the page B B

II

1. magnitude, B = k'I/r (T—tesla)a. k’ = o/2 = 4 x 10-7/2 = 2 x 10-7 T•m/A b. r = distance from wire

2. direction (right hand rule—B) point thumb in direction of current, I point hand toward a side of the wire bend fingers 90o, fingers point in the direction of field,

Bb. straight field in the center of a circular current

into the page out of the page I I

BB

1. magnitude in center of solenoid, B = oI(N/L)N/L = number of loops (N) per length (L)

2. direction (right hand hitch-hiker rule—B) make a fist with thumb sticking out fingers wrap around thumb in direction of current, I

(clockwise or counterclockwise) thumb points in direction of field, B

c. north and south poles on a permanent magnet1. magnetic field lines

2. no monopoles

3. Earth's magnetic field 2. magnetic force, FB

a. moving charge or current in B

B +q v FB

1. magnitudea. FB = qvB

(particle) b. FB = ILB

(current)2. direction (flat hand rule—magnetic force)

right hand for + charge (left hand for – charge) point thumb in direction of v or I point fingers in direction of B palm points in the direction of force, FB

3. other direction rulesWire Loop Parallel Wires

B FB-1 = I1L1B2 = k’I1I2L1/r

I

contract

expand attract

expand contract

repel

b. FB = Fc qvB = mv2/r

B

q + –

B. Induced emf, E1. moving a current loop relative to a magnetic field

generates (induces) an emf, E = B/ta. number of loops (N): E = N(B/t)b. magnetic flux, B = A x B (Wb—Weber)

magnetic field Flux, B, is like rain (B)falling through a loop with

area area, A (maximum when AB)

c. change in magnetic flux, B

1. change A or Ba. increase A by rotating the loop from ||

relative to B (decrease A: ||)b. increase B by moving a magnet toward the

loop or by increasing current in an electro-magnetic (opposite = decrease)

2. induced currenta. I = E/Rb. Lenz's law: the magnetic field that induces

a current and the magnetic field produced by the current are in the opposite direction( FB-induced opposes FB-inducing).

c. direction (flip right hand hitch-hiker rule) make a fist with thumb sticking out pointing in

direction of inducing B flip your thumb over if Bincreases (Lenz's law)

(don't flip if B decreases) fingers wrap around thumb in direction of induced

current, I (clockwise or counterclockwise) summary chart

B Induced Current, I +

– +

– 2. moving a conducting rod through a magnetic field

induces an emf, E = vLB

Steps Algebrastart with substitute A x B for B

substitute Lvt for Aregroupsimplify

E = B/tE = (A x B)/t E = (Lvt x B)/tE = Lv(t/t) x BE = vLB

a. induced current (in rod only), I = E/R = vLB/Rb. direction: use directions above, where increasing

enclosed area = +B (in the diagram: induced current is in rod)

3. conservation of energy and Lenz’s lawa. force needed to move conductor = FB = ILBb. power needed to move conductor, P = FBvav

c. power generated in the circuit, P = IV

d. P = FBvav = IV (conservation of energy)4. transformer, NS/NP = VS/VP = IP/IS

a. device to change voltageb. examples

1. street to home voltage2. battery recharger

Practice ProblemsA. Magnetic Properties

1. Determine the direction of B for the moving charges.Charge velocity side B

a. + east aboveb. + down northc. + south southd. + north easte. + west underf. – south westg. – north aboveh. – down east

2. Determine the direction of B for the currents."Charge" current side B

a. + east aboveb. + north belowc. + up northd. + north easte. + down westf. + east belowg. + west southh. + south above

3. What is the magnitude and direction of magnetic induction, B, at a point 5 cm north from a long wire in which the current is 15 A east?

4. What is the direction of B at the center of a horizontal wire loop carrying a clockwise current?

5. A thin 10-cm-long solenoid has a total of 400 turns of wire and carries a current of 2.0 A. Calculate the field inside near the center.

6. Highlight the correct word.a. Magnetic field lines are (toward or away from) the N

pole of a permanent magnet.b. Magnetic field lines are (toward or away from) the N

geographic pole of the earth. c. The earth's north geographic pole is nearest the

earth's (north or south) magnetic pole. 7. Determine the direction of FB for the following.

v B FB

a. up southb. south downc. east downd. east southe. west eastf. west down

8. Determine the magnitude and direction of the force on an electron traveling 3 x 106 m/s horizontally to the west in a vertically upward magnetic field of strength 1.30 T.

9. Determine the magnitude and direction of the magnetic force on a current segment 5 cm long, placed in an upward magnetic field of strength 1.2 T. The current in the wire is 2500 A to the east.

10. Two long wires, 2 cm apart, carry currents of 100 A in opposite directions. What is the magnitude and direction of magnetic force on a 10-cm length of one wire due to the field of the (very long) other wire?

11. An alpha particle (q = +2e, m = 6.6 x 10-27kg) enters an 2-T magnetic field. The radius of its circular path is 10 mm. Determine the a. velocity.

b. kinetic energy.

c. momentum.

12. The figure shows a cross section of a cathode ray tube. An electron (m = 9.11 x 10-31 kg, q = -1.6 x 10-19 C) initially moves east at a speed of 2 x 107 m/s. The electron is deflected northward by a 6 x l0-4-T magnetic field.

a. What potential difference is needed to accelerate the electron to the given velocity?

b. The direction of the magnetic field is (up or down).c. Determine the magnitude of the magnetic

force on the electron.

d. Determine the radius of curvature of the path followed by the electron while it is in the magnetic field.

An electric field is later established in the same region as the magnetic field such that the electron now passes through the magnetic and electric fields without deflection.e. Determine magnitude and direction of the

electric field.

13. A proton traveling west enters a combined 1000 N/C electric field and a 0.5 T magnetic field. The proton's path is undeflected.

a. What is the direction of the magnetic field, if the electric field is North?

b. What is the velocity of the proton?

14. Determine the magnitude and direction of the magnetic field in the following situations.a. 1 m west of a long wire with a current of 100 A north.

b. A thin 0.50-m-long solenoid has a total of 10,000 turns of wire and carries a current of 6.0 A in a counterclockwise direction.

15. An electron (m = 9.11 x 10-31 kg, q = -1.60 x 10-19 C), traveling west with a velocity of 1 x 106 m/s enters a magnetic field, B = 1 x 10-4 T that is directed up. Determine a. the radius of the circular path.

b. the direction of the path when viewing from above.

16. Wire A carries a 5-A current east. Determine a. the magnitude and direction of the magnetic field

0.5 m north of wire A.

b. the magnitude and direction of the magnetic force on a 0.1 m segment of wire B, carrying a 2-A current west that is 0.5 m to the north of wire A.

17. J. J. Thomson's is credited with discovering the electron. He performed an experiment using the apparatus below to determine the me/qe ratio for an electron.

a. Initial he adjusted the magnetic and electric fields so that the "cathode" rays—electrons would strike the screen at position b.(1) Determine the direction for the

following.B between the clockwise current loops

FB on the electron beamE that would keep the electron beam undeflected

(2) What is the velocity of the electron in terms of the electric field (E) and magnetic field (B)

b. The electric field is turned off.(1) Which path will the electrons follow (a, b or c)?(2) What is the me/qe ratio in terms of B, E and r, the

radius of the electron's curved path.

B. Induced emf, E18. The upward magnetic field through a wire loop changes

from 0 T to 3 T in 0.1 s. The area of the loop is 0.01 m2 and its electrical resistance is 10 . a. DetermineB

E

I

b. What is the direction of current?clockwise

19. A horizontal wire loop with area = 1 m2 and resistance = 5 , is in a 0.5-T, magnetic field. It rotates 90o in 1 s.a. DetermineB

E

I

b. What is the direction of current?

20. A 2-m rod, with an internal resistance of 2 , moves east through an upward magnetic field (B = 2 T) at 10 m/s.

a. Calculate the emf generated by the moving rod

b. Determine the direction of current in the U-shaped rail and rodin the rod

c. Calculate the current through the rod.

d. Calculate the force needed to move the rod.

e. Calculate the power needed to move the rod.

f. Calculate the electric power generated in the circuit.

g. Explain why the answers from parts e and f must be the same.

21. The metal rails of the U-shaped conductor are 1 m apart. A rod moves across the rails at 3 m/s in a vertical magnetic field B = 0.2 T. The resistance is 1 . Determine theI

FB

P

22. The magnetic field surrounding a horizontal wire loop changes from 0 T to 5 T (up) in 0.1 s. The radius of the loop is 0.1 m and its electrical resistance is 10 . Determine a. the induced emf.

b. the magnitude and direction of the induced current as viewed from above.

23. A transformer reduces 120-V ac to 9.0-V dc (a diode changes ac to dc). The secondary coil contains 30 turns and the draws 0.4 A. Calculatea. the number of turns in the primary.

b. the current in the primary.

c. the power transformed.

24. A transformer reduces 120-V to 6.0-V. The secondary coil contains 50 turns and the radio draws 0.25 A. Determinea. the number of turns in the primary.

b. the current in the primary.

c. the power transformed.

Practice Multiple ChoiceBriefly explain why the answer is correct in the space provided.1. An electron is moving south in a downward magnetic field.

What is the direction of the magnetic force on the electron?(A) west (B) east (C) down (D) north

2. What is the direction of the magnetic field north of a wire carrying a current east?(A) west (B) east (C) down (D) up

3. A wire carries a current north in an upward magnetic field. What is the direction of the magnetic force on the wire?(A) down (B) up (C) east (D) west

4. A positively charged particle moves to the right without deflection through a pair of charged plates. Between the plates are a uniform electric field, E = 6 N/C and a uniform magnetic field, B = 2 T, directed as shown.

The speed of the particle is most nearly (A) 1/3 m/s (B) 2/3 m/s (C) 3 m/s (D) 12 m/s

5. A counterclockwise current I in a circular loop of wire is situated in a magnetic field directed out of the page.

What effect does the magnetic force have on the loop?(A) it expands in size (B) it contract in size (C) it rotate about an axis perpendicular to the page (D) it rotate about an axis in the plane of the

page

6. Two parallel wires, each carrying a current I, repel each other with a force F. If both currents are doubled, the force of repulsion is (A) 2F (B) ½F (C) 4F (D) ¼F

7. Two long, parallel wires, fixed in space, carry currents I1 and I2. The force of attraction has magnitude F. What currents will give an attractive force of magnitude 4F? (A) 2I1 and ½I2 (B) I1 and ¼I2

(C) ½I1 and ½I2 (D) 2I1 and 2I2

8. An electron traveling to the right enters a magnetic field directed into the page, as a result, the electron changes direction, but without loss of energy.

Which shows the path that the electron follows? (A) A (B) B (C) C (D) D

9. A metal spring has its ends attached so that it forms a circle. It is placed in a uniform magnetic field.

Which of the following will NOT cause a current to be induced in the spring? (A) Changing the magnitude of the magnetic field(B) Increasing the diameter of the circle by stretching the

spring (C) Rotating the spring about a diameter (D) Moving the spring perpendicular to the

magnetic field

Questions 10-13 A loop of wire has a total resistance of 10 and an area of 0.01 m2. The wire is initially perpendicular to a magnetic field of 5 T directed out of the page. The loop is then rotated 90o so that it is parallel to the magnetic field.

10. Which describes the change in magnetic flux, B? (A) 0.05 Wb to 0 Wb. (B) 0 Wb to 0.05 Wb.(C) 0.5 Wb to 0 Wb. (D) 0 Wb to 0.5 Wb.

11. If the rotation takes 0.01 s, what is the induced emf, E? (A) 50 V (B) 0.5 V (C) 0.05 V (D) 5 V

12. What is the induced current in the loop?(A) 50 A (B) 0.5 A (C) 0.05 A (D) 5 A

13. What is the direction of the induced current? (A) out of the paper (B) into the paper(C) clockwise (D) counterclockwise

14. A rectangular loop of wire is 0.2 m wide with resistance of 20 . One end of the loop is in a downward 2-T magnetic field. The loop is pulled east at 5 m/s.

x x x x x x x x x x x x x xx x x x x x x 0.2 m 5 m/sx x x x x x xx x x x x x x

What are the magnitude and direction of the induced current in the loop?

Magnitude Direction(A) 40 A Clockwise(B) 40 A Counterclockwise(C) 0.1 A Clockwise(D) 0.1 A Counterclockwise

15. In each of the following situations, a bar magnet is aligned along the axis of a conducting loop. The magnet and the loop move with the indicated velocities. In which situation will the bar magnet NOT induce a current in the conducting loop? (A) (B)

(C) (D)

Questions 16-17 A proton (q = 10-19 C, m = 10-27 kg) in a magnetic field (B = 10-1 T) moves in a circle (r = 10-1 m).

16. How much work is done in one complete one revolution? (A) 0 J (B) 10-22 J (C) 10-5 J (D) 102 J

17. Which is the best estimate of the speed (in m/s) of a proton in the beam as it moves in the circle? (A) 10-2 (B) 103 (C) 106 (D) 107

18. A downward magnetic field B is confined to the region of radius a. The induced emf in the wire loop of radius b is E.

What is the induced emf in the wire loop of radius 2b? (A) Zero (B) E/2 (C) E (D) 2 E

19. A wire of constant length is moving in a constant magnetic field, as shown. The wire and the velocity vector are perpendicular to each other and are both perpendicular to the field.

Which graph represents the emf E as a function of v? (A) (B)

(C) (D)

20. Two conducting wire loops move in the directions indicated at the same velocity, v. The wire carries a current, I, in the direction indicated.

Which of the following is true about the induced electric currents, if any, in the loops?

Loop 1 Loop 2(A) No current No current (B) No current Counterclockwise (C) Clockwise No current (D) Clockwise Clockwise

21. The currents in three parallel wires, X, Y, and Z, each have magnitude I and are in the directions shown. Wire Y is closer to wire X than to wire Z.

X Y ZThe magnetic force on wire Y is (A) toward the right (B) into the page(C) out of the page (D) toward the left

Question 22-23 A particle of charge +e and mass m moves with speed v perpendicular to a magnetic field B directed into the page. The path of the particle is a circle of radius r.

22. Which of the following correctly gives the direction of motion and the equation relating v and r?

Direction Equation (A) Clockwise v = eBr/m (B) Clockwise v = (eBr/m)½ (C) Counterclockwise v = eBr/m (D) Counterclockwise v = (eBr/m)½

23. The period of revolution of the particle is(A) mr/eB (B) (m/eB)½

(C) 2m/eB (D) 2(m/eB)½

24. A conducting loop of wire that is initially around a magnet is pulled away from the magnet toward the top of the page inducing a current in the loop. What is the direction of the induced current and the induced magnetic field?

Induced current Induced magnetic field(A) clockwise toward the top (B) clockwise toward the bottom (C) counterclockwise toward the top (D) counterclockwise toward the bottom

25. A sheet of copper in the plane of the page is connected to a battery. The copper sheet is in a magnetic field B directed into the page. P1 and P2 are points at the edges of the strip. B

x x x x x x x x x x x x x x x – P1 x x x P2 E x x x x x + x x x x x x x x x x

Which of the following statements is true? (A) P1 is at a higher potential than P2. (B) P2 is at a higher potential than P1. (C) P1 and P2 are at equal positive potential.(D) P1 and P2 are at equal negative potential.

Practice Free Response1. A square loop of wire of side 0.20 m has a resistance of

0.60 . The loop is positioned in a 0.030-T magnetic field. The field is directed into the page, perpendicular to the plane of the loop.

x x x x x x xx x x x x x xx x x x x x x x x x x x x 0.20 mx x x x x x xx x x x x x xx x x x x x x

a. Calculate the magnetic flux B through the loop.

The field strength now increases to 0.20 T in 0.50 s. b. Calculate the emf E induced in the loop.

c. (1) Calculate the current I induced in the loop.

(2) What is the direction of the current in the loop?

2. The bar of mass M and length D, has a constant current I flowing through it in the northern direction. The space between the thin frictionless rails contains a uniform magnetic field B, perpendicular to the plane of the page. The magnetic field and rails extend for a distance L. The magnetic field exerts a constant force on the bar resulting in its acceleration to the east.

a. In what direction must the magnetic field B point in order to create the magnetic force?

Determine the following. Express answers in terms of the quantities given above.b. acceleration of the bar.

c. speed of the bar as it leaves the end of the track.

Determine the following given the values:B = 5 T L = 10 m I = 200 A M = 0.5 kg D = I0 cm

d. speed of the bar as it reaches the end of the track.

e. the average power to the bar by the electric current.

CuSheet