Question

Circular loop of a wire and a long straight wire carry currents $I_o$ and $I_e$, respectively as shown in figure. Assuming that these are placed in the same plane, the magnetic fields 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 straight wire $=\frac{{\mu }_0{I}_e}{2\pi H}$

Magnetic field due to circular wire $=\frac{{\mu }_0{I}_e}{2R}$

Now $\frac{{\mu }_0{I}_e}{2\pi H}=\frac{{\mu }_0{I}_e}{2R}$

$\Rightarrow H=\frac{R{I}_e}{\pi I_e}$