Moving Charges and Magnetism - Result Question 37
38. 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:
[2012]
(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) $\frac{\mu_0 I}{R}$
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Answer:
Correct Answer: 38. (a)
Solution:
- (a)
The magnetic field, due the coil, carrying current $I$ Ampere
$ B_1=\frac{\mu_0 I}{2 R} $
The magnetic field due to the coil, carrying current $2 I$ Ampere
$B_2=\frac{\mu_0(2 I)}{2 R}$
The resultant $B$
$ \begin{aligned} B _{\text{net }} & =\sqrt{B_1^{2}+B_2^{2}+2 B_1 B_2 \cos \theta}, \theta=90^{\circ} \\ B _{\text{net }} & =\sqrt{B_1^{2}+B_2^{2}}=\frac{\mu_0(2 I)}{2 R} \sqrt{1+4} \\ & =\frac{\sqrt{5} \mu_0 I}{2 R} \end{aligned} $
