A uniform magnetic field B⃗ = (3î + 4ĵ + k̂) Tesla exist in a region of space. A semicircular wire of radius 1 m carrying a current of 1A having its centre at (2, 2, 0) m is placed on the X-Y plane as shown. The force on the semi-circular wire will be

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G1 Physics · Accepted Answer

For any wire in uniform B⃗, net force is I∫dℓ⃗×B⃗=I(r⃗₂-r⃗₁)×B⃗. Using the endpoints of the semicircle shown gives F⃗=√2(î-ĵ+k̂) N. Hence B.