Question

Use Biot Savart law to obtain an expression for the magnetic field at the centre of a coil in the form of a square of sides 2a carrying a current I.

Answer 1

Let O be the centre of a square ABCD of sides 2a as shown in the figure

Magnetic field at O due to side AB 

By symmetry, magnetic field will be same for each side

∴ Total magnetic field at O

B = 4B₁ = \(\frac{4\sqrt2\mu_0I}{4\pi a} = \frac{\sqrt2\mu_0I}{\pi a}\)