Q130 / 200 · NEET 2012 (Screening) · Physics

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

  • Correct answer
    A
    $\frac{\sqrt{5} \mu_0 I}{2 R}$
  • B
    $\frac{3 \mu_0 I}{2 R}$
  • C
    $\frac{\mu_0 I}{2 R}$
  • D
    $\frac{\mu_0 I}{R}$

Solution

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 $\begin{aligned} & =\sqrt{B^2+(2 B)^2}=\sqrt{5 B^2}=\sqrt{5 B} \\ & =\frac{\mu_0 I \sqrt{5}}{2 R} \end{aligned}$

Hence, the correct answer is option: 'A'.

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