The resulting change in flux linkage is NThe resulting change in flux linkage is N (which can (which can be expanded to be expanded to BAN)BAN)

The size of the induced EMF is given byThe size of the induced EMF is given by

NN / / t which can be expanded to ANt which can be expanded to ANB / B / tt

The magnetic flux density B is proportional to the The magnetic flux density B is proportional to the current I supplying the electromagnet.current I supplying the electromagnet.

Therefore the induced EMF is proportional to the rate of Therefore the induced EMF is proportional to the rate of change in current in the electromagnetchange in current in the electromagnet

Consider a rectangular coil which has N turns, a length Consider a rectangular coil which has N turns, a length ll and a width w. The coil is moving with velocity v into a and a width w. The coil is moving with velocity v into a uniform magnetic field which has a flux density Buniform magnetic field which has a flux density B

Velocity v

Uniform magnetic field into page

w

ll

Assume the coil enters the field at time t=0Assume the coil enters the field at time t=0

Time for the coil to enter the field completely Time for the coil to enter the field completely (using s=d/t) is(using s=d/t) is

t = width/speed = w/vt = width/speed = w/v

During this time the flux linkage NDuring this time the flux linkage N increases increases steadily from 0 to BNsteadily from 0 to BNllww

The change in flux linkage each second is given byThe change in flux linkage each second is given by

NN//t = BNt = BNllw/(w/v) = BNw/(w/v) = BNllvv

Once the coil is Once the coil is fullyfully into the field, there is no longer a into the field, there is no longer a change in flux linkage (it is equal to BNlw). Since there is change in flux linkage (it is equal to BNlw). Since there is not change in flux linkage there is no longer an induced not change in flux linkage there is no longer an induced EMF.EMF.

i.e. The EMF induced in the leading side of the coil is cancelled out 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 sideby an equal and opposite EMF induced in the trailing side

The graphs below show how the flux linkage and The graphs below show how the flux linkage and induced EMF change with timeinduced EMF change with time

Flux Linkage Induced EMF

Time Timew/v w/v

BNlw

BNlv

A uniform magnetic field with a flux density of 72mT is A uniform magnetic field with a flux density of 72mT is confined to a region with a width of 60mm. A confined to a region with a width of 60mm. A rectangular coil with a length of 50mm and a width of 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 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. with the longer edge parallel to the edge of the field. CalculateCalculate

The flux linkage when the coil is completely in the field The flux linkage when the coil is completely in the field [1.1mWb][1.1mWb]

The time take for the flux linkage to increase from 0 to the The time take for the flux linkage to increase from 0 to the maximum value maximum value [2.0s][2.0s]

The induced EMF as it enters the field The induced EMF as it enters the field [5.4mV][5.4mV]

Sketch a graph to show how the flux linkage through the coil 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 changes from the instant the coil enters the field to the moment it leaves the field completelyleaves the field completely