A magnetic field in a certain region is given by and a coil of radius a with resistance R is placed in the x-y plane with its center at the origin in the magnetic field (see Fig 6.6) . Find the magnitude and the direction of the current at (a, 0, 0) at

Question

A magnetic field in a certain region is given by

and a coil of radius a with resistance R is placed in the x-y plane with its center at the origin in the magnetic field (see Fig 6.6) . Find the magnitude and the direction of the current at (a, 0, 0) at

Philoid · Accepted Answer

As this sign ⨀ suggest that the direction of magnetic field is outwardly along z-axis. Also in above figure circular plane is in x-y plane and in question given that .

So now area vector is also in ⨀ i.e. same as and area is πa² thus the angle now substituting the values

Now applying faraday’s law,

So

Now this induced e.m.f also produced induced current

We have to find the current at t, t , t putting these values in above equation

Therefore current at

and direction will be along + ĵ

Now current at

Hence current at

I=0

Now at last current at

Hence magnitude of current at

and direction will be along - ĵ