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Two wires are bent (shown as joint-circle) with radius r (in xy plane). The upper half as resistance of $2 R Ω$ and the lower half of $R Ω$ . A current I is passed into circle as shown. The magnetic field at centre is:

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$\frac{μ_{0} I}{2 r} (\hat{k})$

$\frac{μ_{0} I}{12 r} (\hat{k})$

$\frac{μ_{0} I}{r} (\hat{k})$

answer is D.

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Detailed Solution

Magnetic field at centre,

$B_{C} = \frac{μ_{0}}{4 r} [(\frac{2 I}{3}) - (\frac{I}{3})] = \frac{μ_{0} I}{12 r}$

outward so direction is along $\hat{k}$ .

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