(i) Derive an exp

By, Biot-Savart Law, we know that,

The axis, is perpendicular to the plane, so, θ=90˚

r means the distance of the point from current location, i.e. (By, Pythagoras)

has a constant value.

dl is the infinitesimal part of the circular conductor. So, .

Now, by this equation we get the value for dB and by integrating dB we can get B.

But here, a simple visualization tells us that, all the cos components of B, cancel outs as we sum up running through the circular conductor. So, it is only the sin components that will count.

So, By Pythagoras, we know that,

(ii) We know that, magnetic field at center of circular coil is,

Here, n=100, r=10cm, I=1A and

Putting the values and calculating we get,

.

OR

Ampere’s Circuital Theorem: If current passes through a closed path, then Integral of Magnetic Field density along that path is equal to the product of current flowing within with the permeability of that medium.

For r<a,

As we know, I is distributed over , so, in , the amount of current is,

or

For r>a,

or

So, the graph is like,