Question

Two coaxial circular loops `L_1` and `L_2` of radii `3cm` and `4cm` are placed as shown in figure. What should be the magnitude and direction of the current in the loop `L_2` so that the net magnetic field at the point O be zero?

Answer 1

The resultant magnetic field at the point O will be zero only if the direction of current in loo `L_2` is opposite to that in loop `L_1`. Then magnetic field at O due to current `I_1` in loop `L_1`
=magnetic field at O due to current `I_2` in loop `L_2`
or `(mu_0)/(4pi)(2piI_1a_1^2)/((a_1^2+x_1^2)^(3//2))=(mu_0)/(4pi)=(2piI_2a_2^2)/((a_2^2+x_2^2)^(3//2))`
or `(I_1a_1^2)/((a_1^2+x_1^2)^(3//2))=(I_2a_2^2)/((a_2^2+x_2^2)^(3//2))`
or `(1xx(0*03)^2)/([(0*03)^2+(0*04)^2]^(3//2))=(I_2xx(0*04)^2)/([(0*04)^2+(0*03)^2]^(3//2))`
or `I_2=(1xx(0*03)^2)/((0*04)^2)=9/16=0*56A`