1. Fixed Coil in a Changing Magnetic field 1
Consider a small coil with N turns and area A in a magnetic field with flux density B which is supplied by an electromagnet.
If the current supplying the electromagnet is changed then the resulting flux density changes as well. This change the flux linkage through the small coil and an EMF is induced in the small coil
Initial flux linkage
N = BAN
The change in current to the electromagnet causes a small increase in flux density from B to B + B in time t

2. Fixed Coil in a Changing Magnetic field 2
The resulting change in flux linkage is N (which can be expanded to BAN)
The size of the induced EMF is given by
N / t which can be expanded to ANB / t
The magnetic flux density B is proportional to the current I supplying the electromagnet.
Therefore the induced EMF is proportional to the rate of change in current in the electromagnet

3. Rectangular Coil Moving into a Magnetic field 1
Consider a rectangular coil which has N turns, a length l and a width w. The coil is moving with velocity v into a uniform magnetic field which has a flux density B
Assume the coil enters the field at time t=0
Time for the coil to enter the field completely (using s=d/t) is
t = width/speed = w/v
During this time the flux linkage N increases steadily from 0 to BNlw w l
Velocity v
Uniform magnetic field into page

4. Rectangular Coil Moving into a Magnetic field 2
The change in flux linkage each second is given by
N/t = BNlw/(w/v) = BNlv
Once the coil is fully into the field, there is no longer a change in flux linkage (it is equal to BNlw). Since there is not change in flux linkage there is no longer an induced EMF.
i.e. The EMF induced in the leading side of the coil is cancelled out by an equal and opposite EMF induced in the trailing side

5. Rectangular Coil Moving into a Magnetic field 3
The graphs below show how the flux linkage and induced EMF change with time
Flux Linkage
Induced EMF
BNlw
BNlv
Time
w/v
Time
w/v

6. Problems 1
A uniform magnetic field with a flux density of 72mT is confined to a region with a width of 60mm. A rectangular coil with a length of 50mm and a width of 20mm has 15 turns. It is moved into the field at 10 mm/s with the longer edge parallel to the edge of the field. Calculate
The flux linkage when the coil is completely in the field [1.1mWb]
The time take for the flux linkage to increase from 0 to the maximum value [2.0s]
The induced EMF as it enters the field [5.4mV]
Sketch a graph to show how the flux linkage through the coil changes from the instant the coil enters the field to the moment it leaves the field completely