11.1 Electromagnetic Induction

The south pole of a bar magnet is pushed into one end of a coil of wire, which is connected to a sensitive galvanometer as shown:

 

 

A galvanometer measures the amount of current through a moving coil, shown by a deflecting needle. A maximum deflection of the galvanometer needle of 7 units to the right is observed. 

Next, the north pole of the magnet is pushed into the other end of the coil at twice the speed.

What would be the maximum deflection of the galvanometer needle?

A coil with 100 turns and an area of 0.30 m² is set up inside a uniform magnetic field, of magnitude 60 mT.

When the coil spins at a constant rate about the rotation axis, an alternating e.m.f ϵ is induced as shown in the image below:

The magnitude of the induced e.m.f ϵ can be calculated at any time t using the equation:

Which line correctly identifies the best estimate of X and Y?

Υou may use the fact that .

	X / V	Y
A.	2.5	6
B.	6.0	3
C.	2.0	2
D.	5.5	3

A coil is rotated in a uniform magnetic field. An alternating emf is induced in the coil. What is a possible phase relationship between the magnetic flux through the coil and the induced emf in the coil when the variations of both coils are plotted with time?

A straight wire PQ carrying a constant current I is placed perpendicularly to a uniform magnetic field, as represented by the dotted line in the diagram below.

 

The current-carrying wire is then rotated anti-clockwise through an angle θ about an axis perpendicular to the plane of the diagram.

Which of the following graphs shows how the magnitude of the magnetic force F on the wire varies with θ in the rangeradians?

Two circular coils, J and K, share a common axis and are parallel to each other. A constant direct current passes through coil J.

Coil K is moved towards coil J and then moved back to its original position. 

As coil K moves, what is the direction of the current induced in coil K relative to the current in coil J?

	Current direction in coil K when moving towards coil J	Current direction in coil K when moving away from coil J
A.	same direction as J	same direction as J
B.	same direction as J	opposite direction to J
C.	opposite direction to J	same direction as J
D.	opposite direction to J	opposite direction to J

A current I = 200 mA is passed through a pivoted square wire frame, of side length 50 cm, which is initially balanced.

A bar magnet is placed near one of the edges of the frame, which causes it to tilt. A rider of mass m = 10 g and length 10 cm is then placed at the midpoint of the opposite edge on the wire frame, such that the frame regains its balance, as shown in the diagram below.

What is the magnitude of the magnetic flux density near the magnet?

A bar magnet moves steadily from right to left through a very long solenoid.

A galvanometer is connected across the solenoid. A galvanometer measures the amount of current (and voltage) through a moving coil, shown by a deflecting needle.

Which graph shows the deflection of the galvanometer, θ with time, t?

A copper ring is suspended by a long, light rod pivoted at X so that it may swing as a pendulum, as shown in the diagram below:

An electromagnet is set up so that the ring can pass over it as it swings. The ring is then set into oscillation at time t = 0, with switch K open. It completes two full oscillations, at which point the switch K is closed at time t = t₀

Which graph correctly shows the variation of the displacement x with time t?   

 

The Olympic torch can be modelled as a 1.0 m long conducting rod. People jogging can be said to average between 6.4 – 9.7 km h⁻¹.

The torch is carried along streets in towns around the world. On which part of the route shown is the induced e.m.f. at a maximum, and what is the approximate motional e.m.f. induced in the metal of the torch when carried along this street by a brisk jogger?

Assume that the Earth’s field has magnetic flux density, B = 50 µT.

	route	motional e.m.f.
A.	Sempra Lane	125 µV
B.	Moorlands Street	125 nV
C.	Sempra Lane	45 mV
D.	Moorlands Street	45 µV

A length of conducting wire XY is moved downwards through the poles of a horseshoe magnet.

This will change the ends of the wire so that compared to end Y of the wire, end X will have

A square coil of conducting wire with sides of length W is moved at constant speed v left to right, through a uniform magnetic field which is directed into the page and has width W. 

From the point where the coil enters the field until the point where it leaves it, which description best fits the direction of the current induced in the coil?

Three loops of wire are arranged so that the current flowing in loop X in a clockwise direction induces a current in both in loops Y and Z. The three loops are all on the same plane.

What is the direction of the induced currents in loop Y and loop Z?

	Loop Y	Loop Z
A.	clockwise	clockwise
B.	clockwise	anti-clockwise
C.	anti-clockwise	anti-clockwise
D.	anti-clockwise	clockwise

A pendulum made from a flat disk of copper is suspended in a region of uniform magnetic field by an insulating rod connected to a horizontal support. The disk is pulled to one side of the field and then released.

The uniform magnetic field is directed into the plane of the paper.

Which of the following is true for both the direction of the induced current in the disk and the change in amplitude of the oscillations of the pendulum with time?

	Direction of induced current	Change in amplitude
A.	changes	decreases
B.	changes	stays constant
C.	stays constant	decreases
D.	stays constant	stays constant

A flat coil with N turns has a diameter d. The coil has a flux density of B in a direction of 90° to the plane of the coil.

A second coil has 3N turns and diameter 2d.

Select the correct ratio of

The graph shows the variation with angle θ of the magnetic flux φ through a coil that is rotating in a uniform magnetic field. θ is measured between the coil and the plane of the magnetic field lines.

Select the graph which correctly shows the variation in emf, ε with angle θ for the same coil.

A coil of conducting wire having N turns is wrapped around a cardboard cylinder. The ends of the coil are connected using a straight piece of conducting wire. The coil is moved towards a permanent bar magnet fixed in position. The coil moves at velocity v.

The induced current in the straight section of wire is

The solid line on the graph shows the variation with time of a magnetic flux passing through a loop of wire. Both the magnetic field strength and the area of the loop are increased but no other changes are made.

The new graph of magnetic flux and time can be represented by the dashed lines labelled

Two coils are arranged so that one fits inside the other with the axes parallel. The larger coil has 200 turns and cross-sectional area of 30 cm². A changing current in the small coil causes the magnetic field to increase at a rate of 0.5 T s^–1.

The induced emf in the large coil will be