Rankers Physics

Magnetic Field Due to Circular Current Carrying Wire: Practice Problem & Solution

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 2I, respectively. The resultant-magnetic field induction at the center will be: (2012 Pre)
$\frac{\sqrt{5} \mu_0 I}{2 R}$
$\frac{3 \mu_0 I}{2 R}$
$\frac{\mu_0 I}{2 R}$
$\frac{\mu_0 I}{R}$

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Magnetic Field Due to Circular Current Carrying Wire. Understanding the underlying formula is key to arriving at the correct answer below:

The magnetic fields due to the two perpendicular coils are $B_1 = \frac{\mu_0 I}{2R}$ and $B_2 = \frac{\mu_0 (2I)}{2R} = \frac{\mu_0 I}{R}$. Since their planes are at right angles, the fields are perpendicular, so $B_{\text{res}} = \sqrt{B_1^2 + B_2^2} = \frac{\sqrt{5}\mu_0 I}{2R}$.

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