Question

Circular loop of a wire and a long straight wire carry current Ic and Ie 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

The correct option is A

$\frac{I_{e}R}{I_c\pi }$

Magnetic field due to closed loop of radius R
$\overrightarrow{B_1}=\frac{{\mu }_0{I}_c}{2R}$ Out of the plane
Magnetic field due to straight wire carrying current $I_e$
$\overrightarrow{B_2}=\frac{{\mu }_0{I}_e}{2\pi H}⨂$ Into the plane
It is given that ${\overrightarrow{B}}_{net}$ at loop centre is zero
$\overrightarrow{B_1}-\overrightarrow{B_2}=0\overrightarrow{B_1}=\overrightarrow{B_2}\frac{{\mu }_0{I}_c}{2R}=\frac{{\mu }_0{I}_e}{2\pi H}H=\frac{R{I}_e}{\pi I_C}$