NAT ReviewS.Y.2014-2015

2.1 Demonstrate Oersted’s discovery.

He found that magnetism was produced by current – carrying wires.

2.2 Compare the contributions of Faraday and Oersted to electromagnetic theory

• Oersted: He found that magnetism was produced by current – carrying wires.

• Faraday: He concluded that an electric current can be produced by a changing magnetic field.

2.3 Explain electromagnetic induction. 

• Two simple experiments demonstrate that a current can be produced by a changing magnetic field.

• First: consider a loop of wire connected to a galvanometer as shown.

• If a magnet is moved toward the loop, the galvanometer needle will deflect in one direction.

• If a magnet is moved away from the loop, the galvanometer needle will deflect in the opposite direction.

• If the magnet is held stationary relative to the loop, no galvanometer needle deflection is observed.

• The phenomenon of inducing voltage by changing magnetic field in a coil of wire is called electromagnetic induction.

• If the magnet is held stationary and the coil is moved toward or away from the magnet, the galvanometer needle will also deflect.

• From these observations, you can conclude that a current is set up in the circuit as long as there is relative motion between the magnet and the coil.

• This current is set up in the circuit even though there are no batteries in the circuit.

• The current is said to be an induced current, which is produced by an induced EMF.

Faraday’s Experiment• A coil is connected

to a switch and a battery.

• This is called the primary coil and the circuit is called the primary circuit.

• The coil is wrapped around an iron ring to intensify the magnetic field produced by the current through the coil.

Faraday’s Experiment• A second coil, on the

right, is wrapped around the iron ring and is connected to a galvanometer.

• This is secondary coil and the circuit is the secondary circuit.

• There is no battery in the secondary circuit and the secondary circuit is not connected to the primary coil.

Faraday’s Experiment• The only purpose of

this circuit is to detect any current that might be produced by a change in the magnetic field.

• When the switch in the primary circuit is closed, the galvanometer in the secondary circuit deflects in one direction and then returns to zero.

Faraday’s Experiment• When the switch is

opened, the galvanometer deflects in the opposite direction and again returns to zero.

• The galvanometer reads zero when there is a steady current in the primary circuit.

• Faraday concluded that an electric current can be produced by a changing magnetic field.

• A current cannot be produced by a steady magnetic field.

• The current that is produced in the secondary circuit occurs for only an instant while the magnetic field through the secondary coil is changing.

• An induced EMF is produced in the secondary circuit by the changing magnetic field.

• In both experiments, an EMF is induced in a circuit when the magnetic flux through the circuit changes with time.

• Faraday’s Law of Induction: The EMF induced in a circuit is directly proportional to the time rate of change of magnetic flux through the circuit.

– where Φ is the magnetic flux threading the circuit.– Magnetic flux Φm :

dt

dΦ EMF

dABΦm

• The negative sign is a consequence of Lenz’s law and is discussed later (the induced emf opposes the change in the magnetic flux in the circuit).

• If the circuit is a coil consisting of N loops all of the same area and if the flux threads all loops, the induced EMF is:

dt

dΦNEMF

Application of Faraday’s Law• A coil is wrapped with 200 turns of wire on the

perimeter of a square frame of sides 18 cm. Each turn has the same area, equal to that of the frame, and the total resistance of the coil is 2 . A uniform magnetic field is turned on perpendicular to the plane of the coil. If the field changes linearly from 0 to 0.5 Wb/m2 in a time of 0.8 s, find the magnitude of the induced EMF in the coil while the field is changing.Sol. Loop area = (0.18 m)2 = 0.0324 m2

At t = 0 s, the magnetic flux through the loop is 0 since B = 0 T.

Application of Faraday’s Law– At t = 8 s, the magnetic flux through the loop is – Φm = B·A = 0.5 Wb/m2·0.0324 m2 = 0.0162 Wb.

– The magnitude of the induced EMF is:

V4.05EMF

s0s0.8

Wb0Wb0.0162200dt

dΦ EMF

N

Solve: 1. A coil with 25 turns of wire is wrapped on a frame

with a square cross section 1.80 cm on a side. Each turn has the same area, equal to that of the frame, and the total resistance of the coil is 0.350 Ὡ. An applied uniform magnetic field is perpendicular to the plane of the coil. (a) If the field changes uniformly from 0.00 T to 0.500 T in 0.800 s, find the induced emf in the coil while the field is changing. Find (b) the magnitude and (c) the direction of the induced current in the coil while the field is changing.

2. Suppose the magnetic field changes uniformly from 0.500 T to 0.200 T in the next 0.600 s. Compute (a) the induced emf in the coil and (b) the magnitude of induced current.