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Question

Physics Question on Magnetic Effects of Current and Magnetism

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 :
Problem fig

A

2μ0Ia\frac{\sqrt{2} \mu_0 I}{a}

B

μ0I2a\frac{\mu_0 I}{2a}

C

μ0I2a\frac{\mu_0 I}{\sqrt{2} a}

D

2μ0Ia\frac{2 \mu_0 I}{a}

Answer

μ0I2a\frac{\mu_0 I}{\sqrt{2} a}

Explanation

Solution

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

B=μ0I2aB = \frac{\mu_0 I}{2a}

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

Bnet=B2+B2=μ0I2aB_{\text{net}} = \sqrt{B^2 + B^2} = \frac{\mu_0 I}{\sqrt{2}a}