Question

Two co axial circular loop l1 and l2 of radii 3 cm and 4 cm are placed what should be the magnitude and directionof current in loop l2 show that net magnetic field st point o be zero

Answer 1

we know formula of magnetic field at a point on the axis of dipole is given by
$B= \frac{\mu_0Ia^2}{2(a^2+x^2)^{3/2}}$
where a is the radius of the coil, x is the distance of point from the centre of coil.

$\bf{B(l_1)=B(l_2)}$

$\frac{\mu_0I_1(3)^2}{2(3^2+4^2)^{3/2}}=\frac{\mu_0I_2(4)^2}{2(4^2+3^2)^2{3/2}}$

$\frac{I_1}{I_2}=\frac{4^2}{3^2}$

$I_1=\frac{16}{9}I_2$

here we can see that $I_1$ is greater than $I_2$ so, direction of current $I_2$ will just opposite to direction of current $I_1$

Answer 2

Hey!!

Refer the attachment !

NOTE :- For zero magnetic field at O, the currents I1 and I2 should be in same direction, so current I2 should be in opposite directions and satisfy the condition B1 = B2

Thanks !