Question

Two identical circular wires P and Q each of radius R and carrying current 'I' are kept in perpendicular planes such that they have a common centre as show in the figure. Find the magnitude and direction of the net magnetic field at the common centre of two coils

Answer 1

Given, P and Q are perpendicular wires (circular)

Current= I, radius= r

$B_1$= Magnetic field due to loop P at 0

$B_2$= Magnetic field due to loop Q at 0

Therefore resultant magnetic field, $B=\sqrt{B_1^2+B_2^2}$

And symmetrical $⟹B_1=B_2$

$\therefore B^1=\sqrt{2}B=\sqrt{2}\frac{{\mu }_{0}I}{2r}$

$⟹B^1=\frac{{\mu }_{0}I}{\sqrt{2r}}$