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Q.

A symmetric star shaped conducting wire loop is carrying a steady state current I as shown in the figure. The distance between the diametrically opposite vertices of the star is 4a. The magnitude of the magnetic field at the center of the loop is

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a

μ0I4πa63−1

b

μ0I4πa63+1

c

μ0I4πa33−1

d

μ0I4πa32−3

answer is A.

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Detailed Solution

B12=μ0l4πd[sin⁡α+sin⁡β]α=60∘ β=−30∘=μ0I4πd32−12⇒B12=μ0I4πd3−12Also,d=a Total Magnetic field at center =B0=12B12=12×μ0I4πa3−12=μ0l4πa6[3−1]

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