Electromagnetic Induction (CIE A Level Physics)

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A solenoid has a coil C of wire wound tightly about its centre, as shown in Fig. 7.1.

Fig. 7.1

The coil C has 96 turns.
The uniform magnetic flux Φ, in Wb, in the solenoid is given by the expression

Φ = 6.8 × 10^–6 × I

where I is the current, in A, in the solenoid.

Calculate the average electromotive force (e.m.f.) induced in coil C when a current of 3.5 A is reversed in the solenoid in a time of 2.4 ms.

e.m.f. = ................................... V 

The d.c. supply in Fig. 7.1 is now replaced with a sinusoidal alternating supply.

Describe qualitatively the e.m.f. that is now induced in coil C.

A small solenoid of area of cross-section 1.2 × 10⁻³ m² is placed inside a larger solenoid of area of cross-section 7.8 × 10⁻³ m², as shown in FIg. 1.1

Fig. 1.1

The larger solenoid has 800 turns and is attached to a d.c. power supply to create a magnetic field.

The smaller solenoid has 2000 turns.

Compare the magnetic flux in the two solenoids.

Compare the magnetic flux linkage in the two solenoids.

State Lenz's Law of electromagnetic induction.

The terminals of the smaller solenoid are connected together. The smaller solenoid is then removed from the inside of the larger solenoid. 

With reference to magnetic fields, explain why a force is needed to remove the smaller solenoid. 

Define magnetic flux linkage. 

A square coil of wire of side length 10 cm consists of 5 insulated turns. The coil is stationary in a uniform magnetic field. The plane of the coil is perpendicular to the magnetic field, as shown in Fig. 1.1.

The flux density B of the magnetic field varies with time t as shown in Fig. 1.2.

Determine the magnetic flux linkage inside the coil at time t = 0.30 s. Give a unit with your answer.

The procedure in (b) is repeated, but this time the terminals of the coil are connected together. 

State and explain the effect on the coil of connecting the terminals together during the change of magnetic flux density shown in Fig. 1.2.

A coil is connected to a zero-centred ammeter, as shown in Fig. 1.1. A student drops a magnet so that it falls vertically and completely through the coil. 

Fig. 1.1

The student uses a combination of Faraday’s Law and Lenz’s law to explain what happens on the ammeter as the magnet descends. Fig. 1.2 shows a diagram they draw to illustrate their explanation. 

Fig. 1.1

With reference to Faraday’s Law and Lenz’s Law, evaluate the student’s explanation as illustrated in Fig. 1.1.

Use the axes on Fig. 1.3 to sketch a graph of the induced emf  against time t as the magnet falls completely through the coil. You are not required to include values on either axis. 

Fig. 1.3

State and explain the magnitude of the induced emf when the magnet is exactly midway through its descent in the coil.

As part of an introductory lesson to electromagnetic induction, a physics teacher plans a series of experiments for her students to carry out. 

In experiment 1, two metal rings A and B are dropped from the same height between two magnets, as shown in Fig. 1.1. They are identical, apart from a small slit cut in B as shown. 

Fig. 1.1

The teacher asks her students to observe the motion of the two metal rings as they fall between the magnets. 

Describe and explain the motion of A and B as they fall between the magnets.           

You may wish to include sketches in your answer. 

The physics teacher displays a sketch of the variation of induced emf in a coil with time. This is shown in Fig. 1.3. 

Fig. 1.2

The students are asked to use the properties of the graph shown in Fig. 1.3 to determine how it might be reproduced. 

Use the axes provided in Fig. 1.3 to sketch a graph of the magnetic flux linkage Nϕ through the coil between t = 0 to t = t₄ .

Fig. 1.3

The physics teacher reveals that the graph shown in Fig. 1.2 was produced by a coil moving at a constant speed into and out of a uniform magnetic field. They draw a sketch of this motion in three stages, as shown in Fig. 1.4: 

Fig. 1.4

A student disagrees, saying that while the coil is moving across the magnetic field between  to as shown in Fig. 1.4, magnetic field lines are being cut, so there must be an induced emf in the coil. 

Suggest how the teacher should explain what happens within the coil during time   to to improve the student’s understanding.