Structure $- A$ is a half-circle infinite sheet carrying uniform electric current $I$ flowing out of the paper plane. Structure $- B$ is a quarter-circle infinite sheet carrying uniform electric current $I$ flowing out of the paper plane.

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At the center of the circular arc point $- O$ the total magnetic field is pointing to right in both cases

At the center of the circular arc point $- O$ the total magnetic field is pointing to left in both cases

The field strength of structure $- A$ is larger than that of structure $- B$ .

The field strength of structure $- A$ is smaller than that of structure $- B$ .

answer is A, C.

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Detailed Solution

$\int d B = \int_{- ϕ}^{+ ϕ} \frac{μ_{0} k R d θ}{2 π R} (\cos θ \hat{i} - \sin θ \hat{j}) w h e r e k i s t h e c u r r e n t p e r u n i t l e n g t h o f c i r c u l a r a r c . B = \frac{μ_{0} k}{2 π} \times (\sin ϕ + \sin ϕ) I n A, ϕ = \frac{π}{2} . S o B = \frac{μ_{0} k}{π} I n B, ϕ = \frac{π}{4} . S o B' = \frac{μ_{0} k}{\sqrt{2} π}$