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A coil having 100 turns is placed in the magnetic field of 1m wb. Find the average EMF induced if the coil is moved in 0.2 seconds from the given field to a field of 0.4m wb.
0.3 volt
3 volts
10 volts
30 volts
0.3 volt
The average induced EMF in a coil is determined by Faraday's Law of Electromagnetic Induction, which states that the induced EMF is equal to the negative rate of change of magnetic flux linkage. Given N=100 turns, initial flux ╬ж1тАЛ=1┬аm┬аWb=1├Ч10тИТ3┬аWb, final flux ╬ж2тАЛ=0.4┬аm┬аWb=0.4├Ч10тИТ3┬аWb, and time interval ╬Фt=0.2┬аs, the EMF is calculated as e=тИТN╬Фt╬Ф╬жтАЛ.
The average induced EMF in a coil is determined by Faraday's Law of Electromagnetic Induction, which states that the induced EMF is equal to the negative rate of change of magnetic flux linkage. Given N=100 turns, initial flux ╬ж1тАЛ=1┬аm┬аWb=1├Ч10тИТ3┬аWb, final flux ╬ж2тАЛ=0.4┬аm┬аWb=0.4├Ч10тИТ3┬аWb, and time interval ╬Фt=0.2┬аs, the EMF is calculated as e=тИТN╬Фt╬Ф╬жтАЛ.
e=N├Ч╬ФtтИг╬ж2тАЛтИТ╬ж1тАЛтИгтАЛ тАФ Calculating magnitude of average induced EMF
e=100├Ч0.2тИг0.4├Ч10тИТ3тИТ1├Ч10тИТ3тИгтАЛ тАФ Substituting given values
Electromagnetic induction occurs whenever the magnetic flux linking a circuit changes. In this scenario, the transition of the coil between two magnetic field densities results in a flux linkage change, generating an electromotive force proportional to the number of turns and the speed of flux variation.
Magnetic flux is measured in Webers (Wb).
1 m Wb equals 10тИТ3┬аWb.
Lenz's Law defines the polarity, but magnitude calculation depends on the absolute change in flux.
Enables conversion of mechanical motion to electrical energy.
Fundamental principle for transformers and motors.
Energy loss due to eddy currents if the coil core is not laminated.
Induced EMF magnitude is limited by the rate of flux change.
AC Generators and Alternators.
Induction motors and Transformers.
Calculation: e=100├Ч0.20.6├Ч10тИТ3тАЛ=100├Ч0.003=0.3┬аV.
Option B (3 volts) is a common error resulting from a decimal shift mistake in the division process.
A is correct тАФ The calculation 100├Ч0.20.6├Ч10тИТ3тАЛ yields exactly 0.3 volts.
Always convert milli-units to base units (Webers) before substituting into the EMF formula to avoid magnitude errors.
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