Question

Two similar coils of radius $R$ and number of turns $N$ are lying concentrically with their planes at right angles to each other. The currents flowing in them are $I \& I \sqrt{3}$ respectively. Find the magnetic field induction at the center of the coils.

• A. $\frac{2 \mu_{0} NI }{ R }$
• B. $\frac{3 \mu_{0} NIR }{2}$
• C. $\frac{\mu_{0} \text { NIR }}{2}$
• D. $\frac{\mu_{0} NI }{ R }$

Answer 1

Answer: (D)

$B =\sqrt{ B _{1}^{2}+ B _{2}^{2}}$
$B =\frac{\mu_{ o } NI }{2 R } \sqrt{1+3}=\frac{\mu_{ o } NI \times 2}{2 R }$
$B =\frac{\mu_{0} NI }{ R }$