Two similar coils of radius $R$ are lying concentrically with their planes at right angles to each other. The currents flowing in them are $I$ and $2 I$, respectively. The resultant magnetic field induction at the centre will be

Question

Aicharya · Accepted Answer

The magnetic field $(B)$ at the centre of circular current carrying coil of radius $R$ and current $I, B=\frac{\mu_0 I}{2 R}$
Similarly, if current $=2 I$, then
$\text {Magnetic field }=\frac{\mu_0 2 I}{2 R}=2 B$
So, resultant magnetic field
$\begin{aligned}
& =\sqrt{B^2+(2 B)^2}=\sqrt{5 B^2}=\sqrt{5 B} \\
& =\frac{\mu_0 I \sqrt{5}}{2 R}
\end{aligned}$

Two similar coils of radius $R$ are lying concentrically with their planes at right angles to each other.…

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