Question

A loop of wire with cross-sectional area 2 m2 is inserted into a uniform magnetic field with initial strength 2 T. The field is parallel to the axis of the loop. The field begins to grow with time at a rate of 2 Teslas per hour. What is the magnitude of the induced EMF in the loop of wire

Answer 1

The magnitude of the induced emf in the loop of wire,
`e = 0.00112 V`

Step-by-step explanation:

Cross Sectional Area of the loop, A = 2 m²

Magnetic Field Strength, B = 2 T

Rate of change of magnetic field strength, dB/dt = 2 T/hr

dB/dt = 2 * 1/3600

dB/dt = 0.00056 T/s

The induced emf is given by the equation:
`e = (d \phi)/(dt)`

`\phi = BA`

Differentiating both sides with respect to t

`(d \phi)/(dt) = (d(BA))/(dt)\\\\(d \phi)/(dt) = A (dB)/(dt)`

Since
`e = (d \phi)/(dt)`

`e = A (dB)/(dt)\\\\e = 2 * 0.00056\\\\e = 0.00112 V`