Two insulated circular loops A and B of 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 ______.

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Solution

Q.
Two insulated circular loops A and B of 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 ______. [2024]

1 $\frac{\sqrt{2} μ_{0} I}{2 a}$

2 $\frac{μ_{0} I}{2 a}$

3 $\frac{\sqrt{2} μ_{0} I}{a}$

4 $\frac{2 μ_{0} I}{a}$

Ans.
(1)

${\vec{B}}_{A} = \frac{μ_{0} I}{2 a}$

${\vec{B}}_{B} = \frac{μ_{0} I}{2 a}$ $∵$ ${\vec{B}}_{net} = \frac{\sqrt{2} μ_{0} I}{2 a}$

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