Question

Two circular coils X and Y having radii R and R/2 respectively are placed in horizontal plane with their centres coinciding with each other. Coil X has current I flowing through it in the clockwise sense. What must be the current in the coil Y to make the total magnetic field at the centre of two coils zero?

Answer 1

Magnetic field at the center of coil $B=\frac{{\mu }_{o}I}{2R}$

Since, $B_1=B_2$

We get $\frac{I_1}{R_1}=\frac{I_2}{R_2}$

Or $\frac{I}{R}=\frac{I_2}{R/2}$

$⟹I_2=\frac{I}{2}$