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?

1 Answer
May 19, 2018

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