Induction (DP IB Physics: HL): Exam Questions

A copper rod is placed in a region of uniform magnetic field. The rod is moved horizontally along two parallel conducting rails, X and Y.

The rod lies at right angles to the direction of the uniform magnetic field. It moves at constant speed.

The rails are connected at one end by a thin copper wire.

Outline, with reference to the forces acting on electrons, how an emf is generated in the rod.

State what is meant by the rate of change of flux and explain how it applies to this situation.

The length of the rod is 0.8 m and it moves at a speed of 5.7 m s^–1. The induced emf is 9 mV.

Determine the magnitude of the magnetic field strength.

Explain how Lenz’s law relates to the rod moving on the rails.

A bar magnet is attached to a vertical spring and released from rest so that it oscillates along the axis of a fixed horizontal coil. The potential difference (pd) across the coil is measured using a datalogger.

The graph shows the variation with time of the pd measured across the coil from the time the magnet is released to the lowest position of its motion.

The coil has 2200 turns.   

(i) Determine the maximum magnitude of the rate of change of flux linked with the coil.

[2]

(ii) State the fundamental SI unit for your answer to (a)(i).

[1]

Explain, by reference to at least one law of induction, why

(i) the graph becomes negative

[3]

(ii) the two peaks have different magnitudes.

[2]

The magnet oscillates with simple harmonic motion.

Explain why the magnet eventually comes to rest.

The magnet is replaced with one of the same mass but greater magnetic field strength.

State and explain the effect on the amplitude of the oscillations.

A vertical copper rod of length is attached to a horizontal spring so that it oscillates horizontally with simple harmonic motion of period in a uniform magnetic field . The magnetic field is directed into the page.

The graph shows the variation with time of the horizontal displacement of the rod.

Sketch, on separate axes, graphs to show

(i) the variation with time of the horizontal velocity of the rod

[2]

(ii) the variation with time of the emf induced between the ends of the rod.

[2]

The rod has length = 25 cm, and the magnetic field has magnitude = 68 μT. At the equilibrium position, the rod is moving with speed 5.1 m s⁻¹.

Determine the magnitude of the maximum emf induced between the ends of the rod.

The frequency of the oscillations is doubled with no other changes being made.

State and explain the effect this has on the maximum induced emf between the ends of the rod.

A toy car with a magnet attached so that the North pole faces upwards is released from the top of a ramp. The car rolls down the ramp at constant speed. An emf is induced in a coil of wire as the toy and magnet pass underneath it. 

The induced emf is recorded by a datalogger attached to the coil.

The graph shows the variation of induced emf.

(i) Determine the maximum rate of change of flux linkage in the coil.

[1]

(ii) Explain the shape of the graph between points A and B.

[3]

The length of the magnet is 3.0 cm and the diameter of the coil is 1.5 cm.

Using the graph, determine the speed of the car between positions A and B.

The slope of the ramp is increased, making the car accelerate when released. It reaches point A at 1.86 s. 

Apply Faraday's Law to explain how this would affect the induced emf at points A and B.

Sketch a graph to show the new induced emf as the magnet moves from point X to point B.

An electromagnetic braking system uses a metal disk, attached to the wheel of the vehicle so that they rotate together. An electromagnet is placed such that the poles are on either side of the rotating disk, but do not touch it.

When the driver applies the brakes a direct current passes through the coil of the electromagnet.

Explain with reference to appropriate laws of electromagnetic induction how this design can produce a braking effect.

Conventional braking systems use friction pads which are brought into contact with a rotating disk to slow down vehicles.

Distinguish between the electromagnetic and conventional braking systems, identifying at least two advantages and two disadvantage of the electromagnetic system.

Induced current can be used in switching devices. A current in point P is made to flow in a clockwise direction when viewed from position O.

Outline how Lenz's law applies to the direction of the flow of induced current when the switch is opened and then closed.

The coil at P has 50 turns and an area of 15.8 cm². It produces a constant magnetic field of 0.26 T.  The two coils are identical. 

For coil Q

(i) Determine the magnetic flux when Q is positioned at 45^o to the field produced by P.

[1]

(ii) Calculate and explain the induced emf when the magnetic field is changing at a rate of 4.0 T s⁻¹.

[2]

The graph shows the variation with time of the power delivered by an ac generator.

Determine the frequency of rotation of the generator.

Sketch a graph to show the power delivered when the frequency is halved.

A coil rotates in a magnetic field with a frequency of 50 Hz.

Determine the times on the graph at points A, B, C and D.

The diagram below is a representation of a simple dc electric motor. The armature consists of a single rectangular coil and rotates between the poles of a permanent magnet.

The connections between the coil and battery B are not shown. The split ring is labelled C.

For this circuit

(i) Complete the circuit by drawing the missing components onto the diagram.

[1]

(ii) State the direction of the motion of the coil.

[1]

(iii) Describe how the connections from battery B to the split ring enable the coil to rotate continuously in one direction.

[3]

An A.C. generator consists of a coil between two magnets. The coil starts in the vertical position and rotates.

State and explain the shape of the graph of e.m.f. generated by this configuration over time.

A different coil of length 4050 mm and 3700 mm width is now used in the same generator in a magnetic flux density of 0.98 T. The coil has 62 turns and rotates at the same frequency as the previous coil, 25 Hz.

Calculate the magnitude of the e.m.f. generated by the coil when it moves through an angle of 2.0° from an initially horizontal position.

An unmanned probe is in orbit around Jupiter at right angles to the planet's magnetic field. The probe launches a remote measuring device which remains connected to it by a conducting cable.

When the probe and the device are at a distance L the cable is held in a straight line which is also perpendicular to Jupiter's magnetic field. 

For the motion of the cable in the magnetic field

(i) Sketch a labelled diagram to show the cable, field lines and direction of the force on the electrons within the cable.

[2]

(ii) The magnetic field vector B is at an angle θ to the field lines. Deduce an expression for the motional e.m.f. which is induced in the conducting wire.

[3]

This question is about the motional e.m.f. which can be induced in different situations.

A circuit is set up as shown and then the switch is closed so that current can flow. Observations are made for the first 100 ms.

Explain the effects on the electromagnet of the switch being closed. The analysis should make reference to the expected changes in current, e.m.f. and energy.

In an experiment two metal rings A and B are dropped from the same height between two magnets. The rings are identical, apart from a small slit cut in B.

Describe and explain the motion of A and B as they fall between the magnets. The use of sketches to illustrate is encouraged.

In a thought experiment the variation of induced e.m.f. ε in a coil with time is considered.

Students are asked to discuss the properties of the graph shown above to determine how it might be reproduced.

Use the axes provided to sketch a graph of the magnetic flux linkage NΦ through the conductor between t = 0 to t = t₄.

The graph in part (b) was produced using a coil moving at constant speed into and then out of a uniform magnetic field. The motion is represented in the diagram. 

Referring to the stages of the motion, explain why no induced e.m.f. is seen for the section t₂ to t₃ although the coil can be described as 'cutting magnetic field lines' at that time.

An experiment is designed to model an aeroplane flying parallel to the Earth's surface at a constant speed v.

The wingspan of the plane is modelled by a thin metallic rod of length L = 75.0 cm which is connected to a voltmeter. The Earth’s magnetic field is at 70° to the vertical and has a flux density of 1.8 × 10^–4 T.

Determine the speed at which the metal rod would need to be propelled to generate an emf of 0.15 mV across the ends.

A magnet is dropped through a vertical solenoid.

On the axes provided sketch a graph of the expected e.m.f. as time progresses.

Explain the shape of the graph from part (a).

A generator in a hydroelectric plant features a coil rotating in a magnetic field with a constant angular velocity.  

The power output varies over time for a generator rotating with a maximum power output of P₀ and a frequency of 20 Hz.

(i) Sketch the variation of power output with time for a single complete revolution of the coil. Indicate any key values on your axes.

[2]

(ii) Sketch the variation of voltage with time for a single complete revolution of the coil. Indicate any key values on your axes.

[2]

Using Faraday's Law, show that the new power output is 16P₀ if the frequency of the rotation of the coil increases to 80 Hz. 

You may use the following equation

A graph showing the variation in power over time for a different hydroelectric generator is shown below. 

In this generator, when the rate of flow of water from the dam doubles, the frequency of revolution of the coil also doubles.

On the diagram above, sketch a curve showing the new variation in power over time when the flow rate halves.