Question

To measure the magnetic field, one of the method is through a coil of N turns of area A and placed in a permanent magnet to maximize the magnetic flux through the coil. A quick motion of the coil away from the magnet create a flow of charge Q within a time t. If the circuit is closed with a galvanometer, a resistance R is created. Give the expression of:
a) The flux through the loop
b) The current through the coil
c) The magnetic field around the coil
d) Explain the overtime variation in magnetic field and so the charge variation, including drawing. 10 pts

Answer 1

Assuming B as the magnetic field

a) Magnetic flux through the one loop will be

= BA

and net flux through all loops will be

= NBA

b) the average current in this time interval will be

I = Q/t

c) The change in magnetic flux is the induced emf in the loop;

e = d/dt = NBA/t

and e/R = I

=>e/R = Q/t

=> NBA/Rt = Q/t

=> B = QR/NA

d) The charge Q only depends on the magnetic field, it does not depend on time. The more you increase the magnetic field the more is the charge induced. In overtime situation the induced current will also produce as magnetic field opposing the magnetic flux through the magnetic field reducing the magnetic field through loop and thus reducing the charge on it as well.