Current I₀ enters a circular wire loop of radius r at the top point A and leaves at the bottom point C. The resistance of semicircular path ABC is half that of ADC. Determine the magnetic field magnitude at centre O. Image
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Question

Current I₀ enters a circular wire loop of radius r at the top point A and leaves at the bottom point C. The resistance of semicircular path ABC is half that of ADC. Determine the magnetic field magnitude at centre O. Image

Options

G1 Physics · Accepted Answer

Step 1: Let resistance of ABC = R and resistance of ADC = 2R. The two semicircles are parallel between A and C. Step 2: Current division gives I(ABC) = 2I₀/3 and I(ADC) = I₀/3. Step 3: Field at centre due to semicircle radius r carrying current I is B = μ₀I/(4r). Step 4: The currents around the two semicircles circulate oppositely about O, so their magnetic fields oppose. Step 5: Net magnitude = μ₀/(4r) × |2I₀/3 − I₀/3| = μ₀I₀/(12r). Final answer: μ₀I₀/(12r) (Option A).