Question

Circular loop of a wire and a long straight wire carry currents $I_c$ and $I_e$, respectively as shown in figure. Assuming 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
$B_1=\frac{{\mu }_0{I}_c}{2R}$
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,
$B_1=B_2$
$\frac{{\mu }_0{I}_c}{2R}=\frac{{\mu }_0{I}_e}{2\pi H}$
$\Rightarrow H=\frac{I_{e}R}{\pi I_c}$