Question
Physics Question on Electromagnetic induction
A coil of 200 turns and area 0.20m2 is rotated at half a revolution per second and is placed in a uniform magnetic field of 0.01T perpendicular to the axis of rotation of the coil. The maximum voltage generated in the coil is β2πvolt.The value of β is:
Given: - Number of turns: N=200 - Area of the coil: A=0.20m2 - Magnetic field: B=0.01T - Frequency of rotation: f=0.5Hz
Step 1: Calculating the Angular Velocity
The angular velocity ω is given by:
ω=2πf
Substituting the given frequency:
ω=2π×0.5=πrad/s
Step 2: Calculating the Maximum EMF
The maximum induced EMF (voltage) in the rotating coil is given by Faraday's law of electromagnetic induction:
EMFmax=NABω
Substituting the given values:
EMFmax=200×0.20m2×0.01T×πrad/s EMFmax=200×0.002×π EMFmax=0.4πvolt
Step 3: Relating the Maximum EMF to the Given Expression
The given expression for the maximum voltage is:
EMFmax=β2πvolt
Equating the two expressions:
0.4π=β2π
Cancelling π from both sides:
0.4=β2
Rearranging to find β:
β=0.42 β=5
Conclusion:
The value of β is 5.