Question

Circular loop of a wire an $d$ a long straight wire carry currents $I_c$ and $I_e$, respectively, as shown in figure. Assume that these are placed in the same plane. The magnetic field will be zero at the centre of the loop when the separation $H$ is

• A. $\frac{I_e R}{I_c \pi}$
• B. $\frac{I_c R}{I_e \pi}$
• C. $\frac{\pi I_c}{I_e R}$
• D. $\frac{I_e \pi}{I_c R}$

Answer 1

Answer: (A)

Magnetic field at the centre $O$ of the loop of radius $R$ is given by
$B_1=\frac{\mu_0 I_c}{2 R}$
where $I_c$ is the current flowing in the loop. Magnetic field due to straight current carrying wire at a distance $H$, i.e., at the point $O$ is given by
$B_2=\frac{\mu_0 I_e}{2 \pi H}$
For magnetic field to be zero at the centre of the loop,
$B_1=B_2$
i.e., $ \frac{\mu_0 I_c}{2 R}=\frac{\mu_0 I_e}{2 \pi H}$
$\Rightarrow H=\frac{I_e R}{\pi I_c}$