Question

(a) State Biot—Savart law and express this law in the vector form.
(b) Two identical circular coils, P and Q each of radius R, carrying currents 1 A and $\sqrt{3}$ A respectively, are placed concentrically and perpendicular to each other lying in the XY and YZ planes. Find the magnitude and direction of the net magnetic field at the centre of the coils.

Answer 1

We know that,
$B=\frac{{\mu }_0}{2R}I$
$B_1=\frac{{\mu }_0}{2R}.1B_2=\frac{{\mu }_0}{2R}.\sqrt{3}$
$B=\sqrt{B_1^2+B_2^2}$
$=\sqrt{{\left(\frac{{\mu }_0}{2R}\right)}^2+{(\frac{{\mu }_0}{2R}.\sqrt{3})}^2}B=\frac{{\mu }_0}{2R}\sqrt{1+3}=\frac{{\mu }_0}{2R}.\sqrt{4}B=\frac{{\mu }_0}{R}tan\theta =\frac{B_1}{B_2}=\frac{1}{\sqrt{3}}\Rightarrow \theta ={30}^{\circ }$