Question

Two insulated circular loop A and B radius ‘a’ carrying a current of ‘I’ in the anti clockwise direction as shown in figure. The magnitude of the magnetic induction at the centre will be :

• A. \( \frac{\sqrt{2} \mu_0 I}{a} \)
• B. \( \frac{\mu_0 I}{2a} \)
• C. \( \frac{\mu_0 I}{\sqrt{2} a} \)
• D. \( \frac{2 \mu_0 I}{a} \)

Answer 1

The Correct Option is C

Calculate the magnetic field at the center due to one loop:

\[ B = \frac{\mu_0 I}{2a} \]

Since there are two loops in perpendicular planes, the resultant magnetic field is:

\[ B_{\text{net}} = \sqrt{B^2 + B^2} = \frac{\mu_0 I}{\sqrt{2}a} \]