Question

State Biot Savart Law. Use this law to obtain a formula for magnetic field at the centre of a circular loop of radius $R$, number of turns $N$ carrying current $I$. Sketch the magnetic field lines for a current loop clearly indicating the direction of the field.

Answer 1

The Biot-Savart Law is an equation that describes the magnetic field created by a current-carrying wire, and allows you to calculate its strength at various points.

Here,

I= current in the loop

R= radius of the loop

X= distance between O and P

dl= conducting element of the loop

According to the Biot-Savart law,

Magnetic Field at a point P is,

Again,

dB has two components: dB_x and dB_y

dB_y is cancelled out and the x-component remains.

Therefore

Thus, summation of dl over the loop is given by:

For $Nturns$, $B=\frac{{\mu }_{o}NI{R}^2}{2(x^2+R^2{)}^{3/2}}$

Magnetic field lines due to a circular current carrying coil is,