Electromagnetic Induction

1. ACJC_08H2P1_Q31 The diagram below shows a flat coil placed in a uniform magnetic field. The angle θ is the angle between the plane of the coil and the magnetic field.

What must be the value of θ such that magnetic flux through the coil is the greatest?

A 0 B 45 C 60 D 90

--------------------------------------------------------------------------------------------------------------------- 2. ACJC_08H2P1_Q32 The setup on the below shows a magnet suspended by two 1 m strings oscillating in single plane above a search coil.

Which of the following graphs best represents how the potential difference V across the terminals of the search coil varies with time?

ANS: (C)

3. ACJC_Physics Prelim_H2P1_Q29 The diagram below shows a wire conductor, RS, positioned perpendicular to a uniform magnetic field directed into the paper.

What is the direction in which the wire could be moved at a constant speed to produce the maximum potential difference across its ends, R and S? A perpendicular to only the magnetic field B perpendicular to only the length of the wire C perpendicular to both the length of the wire and the magnetic field D in the direction 45° to the length of the wire

--------------------------------------------------------------------------------------------------------------------- 4. ACJC_Physics Prelim_H2P1_Q31 A metal rod is moved across a magnetic field as shown in the diagram below. Which one of the factors would not affect the value of the induced e.m.f. across the rod?

A The length of the rod B The thickness of the rod C The magnetic flux density of the field D The speed with which the rod moves across the magnetic field

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5. ACJC_Physics Prelim_H2P1_Q32 When a small cylindrical magnet is released from rest at the top of a copper pipe, the magnet falls very slowly through the pipe.

Which of the following does not help to slow down the motion of the magnet as it falls through the same length of the pipe? A Use a pipe with a thinner layer B Use a pipe of material with lower resistivity C Use a stronger magnet of the same mass D Use a lighter magnet

------------------------------------------------------------------------------------------------------------ 6. CJC_2008 Physics Prelim_H2P1_Q32 A straight, horizontal, current-carrying wire lies at right angles to a horizontal magnetic field. The field exerts a vertical force of 8.0 mN on the wire. The wire is rotated, in its horizontal plane, through 30° as shown. The flux density of the magnetic field is halved.

What is the vertical force on the wire?

A 2.0 mN B 3.5 mN C 4.6 mN D 8.0 mN

Reason:

--------------------------------------------------------------------------------------------------------------------- 7. IJC_2008 Physics Prelim_H2P1_Q30 A 50-loop circular coil has a radius of 3.0 cm. It is oriented such that the field lines of a magnetic field are normal to the area of the coil. The magnetic field strength is increased steadily from 0.10 T to 0.35 T in a time of 2.0 s. Find the average induced e.m.f in the coil.

A 43.5 10 V

B 21.8 10 V

C 3.5 V

D 21.8 10 V

Reason:

--------------------------------------------------------------------------------------------------------------------- 8. IJC_2008 Physics Prelim_H2P1_Q31 In the electromagnetic brake as shown below, which of the following forces is eventually responsible in causing the vehicle to slow down?

A Electromotive force produced in the metal disc B Frictional force due to the contact of the axle and the metal disc C Centripetal force acting on the current-carrying metal disc D Magnetic force acting on the current-carrying metal disc Reason: The working principle of an electromagnet is as follows: A metal disc driven by the axle of the wheels is positioned between the poles of an electromagnet. When the brake is stepped, the electromagnet is switched on. Subsequently, the rotation of the disc in the magnetic field causes an e.m.f. to be induced between the rim and the centre of the disc. Currents are, in turn, induced. A magnetic force will act on the current-carrying disc to oppose its motion and hence cause the vehicle to slow down. --------------------------------------------------------------------------------------------------------------------- 9. JJC_2008 Physics Prelim_H2P1_Q30 A single circular loop of wire is placed in a uniform magnetic field of 1.2 T that is normal to the plane of the loop. The area of the loop varies with respect to time as shown in the figure below. What is the e.m.f. induced?

A -31.2 10 V

B -32.4 10 V

C -33.6 10 V

D -37.2 10 V

Reason:

--------------------------------------------------------------------------------------------------------------------- 10. JJC_2008 Physics Prelim_H2P1_Q31 Which of the following statements best describes the motion of the suspended ring immediately after the switch is closed as shown in the figure below?

A The ring remains motionless.

B The ring is repelled.

C The ring is attracted towards the solenoid.

D The ring oscillates towards and away from the solenoid.

Reason: When switch closes, the solenoid becomes a magnet. By Lenz’s Law, a current will be induced in the aluminum ring such that its effect is to oppose the effect of the ‘sudden appearance’ of a magnet, hence the ring is repelled immediately after the switch is closed. ---------------------------------------------------------------------------------------------------------------------

11. PJC_2008 Physics Prelim_H2P1_Q28 A straight wire AB is moved across a magnetic field causing a current to be induced in the direction shown in the diagram.

Which direction did the wire move?

A to the left B to the right C into the plane D out of the plane

Reason: By Fleming right hand rule, the wire must be moving out of the plane to induce a current as shown in the Fig. --------------------------------------------------------------------------------------------------------------------- 12. PJC_2008 Physics Prelim_H2P1_Q29 A sinusoidal magnetic field, B, is applied perpendicular to the plane of a small flat coil of

copper wire. The equation for the changing flux density is given by 0

2sinB B

T

,

where 0B is the amplitude and T, the period of the sinusoidal magnetic field. At which

time, t, is the magnitude of the e.m.f. induced in the coil a maximum?

A T/8 B T/4 C 3T/8 D T/2

Reason:

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13. RJC_2008 Physics Prelim_H2P1_Q31 Two vertical loops A and B, parallel to each other are centred on the same horizontal line, perpendicular to both the vertical planes of A and B as shown in the figure below.

Loop A is fixed and loop B is free to move. Initially, switch S is closed. Just after switch S is opened, loop B will

A move upward

B move downward

C be repelled by loop A

D be attracted to loop A

--------------------------------------------------------------------------------------------------------------------- 14. SAJC_2008 Physics Prelim_H2P1_Q29 A bar magnet is held above the centre of a wire loop in a horizontal plane as shown in the figure below.

The magnet is then dropped with the south end directed toward the loop. Which of the following shows the correct directions for the current induced while the magnet is falling toward the loop and after the magnet has passed through the loop and moves away from it?

--------------------------------------------------------------------------------------------------------------------- 15. SAJC_2008 Physics Prelim_H2P1_Q30 Which of the following statements best describes the motion of the suspended ring as shown in the figure below when a large alternating current is passed through the solenoid?

A The ring remains stationary. B The ring will be attracted towards the solenoid. C The ring rotates about the axis of the thread suspending it. D The ring moves back and forth from the solenoid.

--------------------------------------------------------------------------------------------------------------------- 16. YJC_2008 Physics Prelim_H2P1_Q28 Two parallel rails with negligible resistance are 10.0 cm apart and are connected by a 5.00 W resistor. The circuit also contains a metal rod of resistance 15.0 W sliding at a constant speed of 2.00 m s−1 along the rails as shown below.

A uniform magnetic field B of flux density 10.0 mT is applied perpendicularly to the plane of the rails. Determine the current in the 5.00 W resistor.

Magnet falling toward loop Magnet moves away from loop

A Clockwise Clockwise

B Clockwise Anti-clockwise

C Anti-clockwise Anti-clockwise

D Anti-clockwise Clockwise

A 0.100 A C 41.33 10 A

B 44.00 10 A D

41.00 10 A

--------------------------------------------------------------------------------------------------------------------- 17. YJC_2008 Physics Prelim_H2P1_Q29 A bar magnet is dropped from rest vertically into a solenoid connected to a sensitive voltage sensor. The entire body of the magnet spent a time of 2t inside the solenoid. Which of the following graphs best represents the time variation of the voltage, V recorded by the sensor?

ANS: (D) ---------------------------------------------------------------------------------------------------------------------

18. SRJC_2008 Physics Prelim_H2P1_Q31 ABCD is a wire frame in the shape of an isosceles trapezium (i.e. length AB = length CD), enters a magnetic field with flux density B at t = 0 as shown in the figure below.

If the total resistance of the wire frame is R, what is the value of the induced current in the wire frame after time t seconds, assuming that the frame has not entered the field completely by then?

A 0

B 2 sin

Bvvt l

R

C 2

tan

Bv vtl

R

D B v

Reason:

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19. SRJC_2008 Physics Prelim_H2P1_Q32 A plane circular coil of 30 turns, each of diameter 1.0 cm, rotates 1800 times each minute about a diameter which is perpendicular to a uniform magnetic field of flux

density 4.0 × 10－5 T. What is the maximum instantaneous value of the induced

electromotive force?

A 0.0 V

B 62.8 10 V

C 51.8 10 V

D 52.3 10 V

Reasoning:

--------------------------------------------------------------------------------------------------------------------- 20. MJC_2008 Physics Prelim_H2P1_Q31 A rectangular coil moves in the direction parallel to a long straight current carrying conductor as shown below.

The conductor carries a steady direct current. Which of the following statements is true? A There is no induced current in the coil.

B The induced current flows clockwise in the coil.

C The magnitude of the induced current is proportional to

1

2.

D The magnitude of the induced current in the coil varies with the speed at which the coil is moving.

Reasoning: The change of magnetic flux linkage is a constant. Hence induced emf is zero. --------------------------------------------------------------------------------------------------------------------- 21. MJC_2008 Physics Prelim_H2P1_Q32 A breathing monitoring device consists of a coil of 80 turns wrapped around a patient’s chest. As the patient inhales, the area of the coil is observed to increase from 0.120 m2 to 0.124 m2. The Earth’s magnetic flux density is 50 μT and makes an angle of 22.5° with the axis of the coil.

If the patient inhales in a time interval of 1.59 s, what is the average e.m.f. induced in the coil during the inhalation?

A 3.9 μV B 9.3 μV C 10.1 μV D 22 μV

Reasoning:

------------------------------------------------------------------------------------------------------------ 22. DHS_2008 Physics Prelim_H2P1_Q31 Krystal pushes a short bar of magnet at a constant speed through a long solenoid. A galvanometer is connected across the solenoid.

Which graph best represents the variation of the galvanometer deflection θ with time t?

ANS (A) Assume: Strength of the magnet is strong such that its strength does not vary much over short distances, magnet starts near solenoid at a constant speed. Before magnet enters solenoid, it approaches the solenoid at a constant speed. Rate of change of magnetic flux linking the solenoid is thus constant. Induced e.m.f and hence induced current is constant. Induced current will flow in an anticlockwise manner (for an observer looking from the side i.e. looking at the cross section of the solenoid). As magnet enters the solenoid, induced current will flow in an anticlockwise direction (cross sectional view) in the part of the solenoid in front of the N pole of the magnet Induced current will flow in a clockwise manner (cross sectional view) in part of the solenoid behind the S pole of the magnet. The net current flows in an anticlockwise direction (cross sectional view) as the magnet moves towards the centre but decreases as it does so. The net current flow will be zero when the magnet is at the centre of the solenoid. The net current flows in a clockwise direction (cross sectional view) as it moves away from the centre of the solenoid and increases as it does so. As magnet leaves solenoid at constant speed, induced current is constant and flows in clockwise direction (cross sectional view). (if we don’t assume the strength of the magnet is constant over short distances (which suggests option A, why should the graph be linear in the first place?) ------------------------------------------------------------------------------------------------------------

23. DHS_2008 Physics Prelim_H2P1_Q32 A square coil is placed in a region of uniform magnetic field as shown below. Soke May then moves the coil from A to B.

Which of the following statements correctly describe the e.m.f. induced in the coil?

A There is no e.m.f. induced because the total magnetic flux linking the circuit is the same.

B There is no e.m.f. induced because the velocity of the coil is perpendicular to the magnetic field

C E.m.f. is induced in the coil and it is proportional to the rate of change of displacement of the coil

D E.m.f. is induced in the coil and it is inversely proportional to the rate of change of displacement of the coil

--------------------------------------------------------------------------------------------------------------------- 24. NJC_2008 Physics Prelim_H2P1_Q31

In the above figure, a copper disc rotates uniformly between the pole-pieces of a powerful magnet (not shown in figure) in a clockwise direction. P and Q are metallic brushes making contact with the axle and the edge of the disc respectively. Which of the following statements is correct?

A No current flows through R because there is no flux change through the disc. B No current flows through R because P and Q are at the same horizontal level. C A steady current flows from P, through R, to Q. D A steady current flows from Q, through R, to P. --------------------------------------------------------------------------------------------------------------------- 25. NYJC_2008 Physics Prelim_H2P1_Q32 The diagram shows a magnet standing on the bottom of a dish filled with a conducting solution. A copper wire is suspended freely from a point above the magnet with its tip in the conducting solution. It is held in the position shown The switch is closed and the wire released.Which of the following will be observed?

A The wire will rotate about the magnet.

B The wire will be attracted to the magnet.

C The magnet will rotate about its vertical axis.

D The solution in the dish will rotate about the magnet.

No answer provided. The electrons passing through the solution (between the two wires will experience a force into the page (assuming magnetic field at that point to be downwards) but does that mean that the solution will rotate? Also, current within the solution could be carried by both positive ions and negative ions (not too sure about this). The forces acting on positive and negative ions are opposite, will there still be a net flow of the solution? Electrons flowing in the top part of the tilted wire will experience a force out of the page (Assuming magnetic field to be pointing up) while electrons in the bottom part of the wire will experience a force into the page (assuming magnetic field at that point to be pointing down) so does that mean the titled wire will bend out of the page but diagram is 2D or 3D? Question seems ambiguous from my point of view. ---------------------------------------------------------------------------------------------------------------------

26. NYJC_2008 Physics Prelim_H2P1_Q23 A square loop of wire, in a uniform magnetic field, is rotating at a constant rate about an axis as shown. The magnetic field is directed out of the plane of the page. At time t = 0 the plane of the loop is perpendicular to the magnetic field and side XY is moving out of the page.

Which graph best represents the variation of the magnetic flux through the loop with time?

ANS: (C) ---------------------------------------------------------------------------------------------------------------------

X

Y

A B

C D

27. VJC_2008 Physics Prelim_H2P1_Q30 A closed wire loop in the form of a square of area is mounted with its plane horizontal.

The loop has a resistance of 32.0 10 . The loop is situated in a magnetic field of

strength 0.70 T directed vertically downwards. When the field is switched off, it decreases to zero at a uniform rate in 0.80 s. What is the energy dissipated in the loop during the change in magnetic field.?

A 43.9 10 J

B 47.8 10 J

C 49.8 10 J

D 416 10 J

--------------------------------------------------------------------------------------------------------------------- 28. TJC_2008 Physics Prelim_H2P2_Q3b A glass U-tube containing liquid sodium is constructed from a hollow tubing having a

square cross-section as shown in the figure below.

Electrodes are set into the upper and lower faces of the horizontal section and a current

I is passed through the electrodes. A uniform horizontal magnetic field is applied at right

angles to the axis of the horizontal section of the tube. A magnetic force is then exerted

on the liquid due to the magnetic field.

This technique has been used as a means of pumping liquids. Explain why the energy

required to maintain the current is larger when the liquid is in motion than when

stationary.

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29. TJC_2008 Physics Prelim_H2P2_Q5

(a) A bar magnet with its axis along a coil axis, is released from rest at a position above

the fixed coil so that it drops through the coil as shown in Fig. 5.1. The terminals of

the coil are connected to a data logger which records the induced e.m.f. at regular

intervals. The variation of the induced e.m.f. with time is shown in Fig. 5.2.

Explain, using the laws of electromagnetic induction, why

(i) two momentary deflections in opposite directions are observed, [2]

(ii) the second momentary deflection is larger than the first. [2]

(b) In Fig.5.3, the magnetic field has a uniform flux density of 42.0 10 T and is

directed out the paper. A wire coil placed at P is in the plane of the paper and away

from the field. The coil has 200 turns, a total resistance of 2.0 Ω and an area of 10

cm2. The coil is moved from P to R in 0.20 s.

(i) Calculate the charge which flows in the coil. [2]

(ii) Discuss whether there would be any effect on the charge flow for each of the

following changes:

(a) Increasing the number of turns in the coil. [1]

(b) Increasing the time to move it. [1]

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30. SAJC_2008 Physics Prelim_H2P2_Q5

(a) State the laws of electromagnetic induction.

(b) The magnetic field shown in Fig. 5.1 below has a uniform magnitude of 25.0 mT

directed into the paper. The initial diameter of the loop is 2.00 cm.

(i) The wire is quickly pulled taut, and the loop shrinks to a diameter of zero in 50.0

ms.

1. Determine the average voltage induced between endpoints A and B.

[2]

2. State and explain whether the potential at A is higher or lower than the

potential at B. [3]

(ii) Suppose the loop is undisturbed, but the magnetic field increases to 100 mT in

4.00 × 10-3 s. Determine the average voltage across terminals A and B during

this period. [2]