Question

A circular coil (10 turns, diameter = 25 cm) is placed perpendicular to a uniform magnetic field (B = 2.7 x 10-3 T). If the direction of the magnetic field is reversed in 0.30s, what is the average emf induced in the coil?

Answer 1

`bar mathcal E approx 9 m V`

Explanation:

Faraday's Law for induction in a coil:

• `mathcal E = - N(d Phi)/(d t)`

And `Phi = BA`:

• `implies mathcal E = - NA(d B)/(d t)`

The question does not specify the manner in which the B-field is reversed wrt time - linear, sinusoid or something very different but smooth.

We can generalize:

• `B = B(t)`

• `B(0) = B_o`

• `B(0.3) = - B_o`

For the average value of `mathcal E`:

`bar mathcal E = (int_0^(0.3) \ mathcal E \ dt)/(0.3 - 0)`

`= - NA (int_0^(0.3) \ dot B \ dt)/(0.3 - 0)`

`= - NA( (B(0.3) - B(0) )/(0.3 - 0))`

`= 20/3 NA B_o`

`= 20/3 * 10 * (pi * 0.25^2)/4 * 2.7 times 10^(-3) approx 9 m V`