Question

(i) Use Biot-Savart law to derive the expression for the magnetic field due to a circular coil of radius R having N turns at a point on the axis at a distance 'x' from its centre. 

Draw the magnetic field lines due to this coil.

(ii) A current 'I' enters a uniform circular loop of radius 'R' at point M and flows out at N as shown in the figure.

Obtain the net magnetic field at the centre of the loop.

Answer 1

According to Biot- Savart law,

.'.  Net contribution along x-direction

(ii) Let current I be divided at point M into two parts I₁, and I₂ ; in bigger and smaller parts of the loop respectively.

Magnetic field of current I, at point O

Magnetic field of current I₂, at point O

But I₁ = 3I₂, (As resistance of bigger part is three times that of the smaller part of the loop.) 

Substituting I₁ = 3I₂  in equation (i)