Question

A 45 turn, 2.9 cm diameter coil is inside a pulsed magnet that has been off for some time, so the magnet can cool down. The magnet is turned on, and the magnetic field increases as B(t) = B_max [1 − e^{−3.1 t} ], where t is in seconds and B_max = 31.9 T. The field is perpendicular to the plane of the coil. What is the magnitude of the EMF induced in the coil at t = 0.403 s after the magnet is turned on?

Answer 1

According to Faraday's law, the magnitude of the EMF induced in a coil is:

where is the magnitude of the induced emf, N is the number of turns in the coil, and is the flux of magnetic field through the coil.

Since the field is perpendicular to the coil, flux is just :

where A is the area of the coil.

    (because they give you the diameter, so r=d/2, and you need it in meter).

So the area is:

To find , we need the initial and final values of the magnetic field.

It starts at B=0, so

To find the final flux, you need the magnetic field at the final time t = 0.403s:

So the emf is: