Question 13

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:

Solution

$$B_1 = B_2 = \frac{\mu_0 I}{2a}$$

$$B_{\text{net}} = \sqrt{B_1^2 + B_2^2}$$ ($$B_1$$ and $$B_2$$ are perpendicular vectors)

$$B_{\text{net}} = \sqrt{\left(\frac{\mu_0 I}{2a}\right)^2 + \left(\frac{\mu_0 I}{2a}\right)^2} \implies B_{\text{net}} = \sqrt{2} \cdot \frac{\mu_0 I}{2a} = \frac{\mu_0 I}{\sqrt{2}a}$$

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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:

Solution

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