Question

Two similar coils of radius $R$ are lying concentrically with their planes at right angles to each other, if the current through them are $2I$ and $4I$ respectively, then net magnetic induction at the centre is

• A. $\frac{\sqrt{5}{\mu }_{0}I}{R}$
• B. $\frac{\sqrt{5}{\mu }_{0}I}{2R}$
• C. $\frac{{\mu }_{0}I}{R}$
• D. $\frac{{\mu }_{0}I}{2R}$

Answer 1

The correct option is A $\frac{\sqrt{5}{\mu }_{0}I}{R}$

The magnetic induction at the centre $O$ will be,


$B_1=\frac{{\mu }_0\left(2I\right)}{2R}$ and $B_2=\frac{{\mu }_0\left(4I\right)}{2R}$
Since $B_1$ and $B_2$ are perpendicular,
$B_{net}=\sqrt{B_1^2+B_2^2}=\sqrt{{\left(\frac{{\mu }_{0}I}{R}\right)}^2+{\left(\frac{2{\mu }_{0}I}{R}\right)}^2}\Rightarrow B_{net}=\frac{\sqrt{5}{\mu }_{0}I}{R}$