A current I enters a square loop ABCD of side a at A and leaves at C. Resistance of path ABC is r, while resistance of path ADC is 2r. The magnitude of the magnetic field at the centre of the square is:

Question

G1 Physics · Accepted Answer

The current divides inversely in proportion to branch resistance. For branch ABC of resistance r and branch ADC of resistance 2r: i₁ = 2I/3, i₂ = I/3. Each side of the square subtends 45° at the centre on either end. Magnetic field at the centre due to one side carrying current i is B s i d e B_side B s ​ i d e = [μ₀i/(4π(a/2))](sin45° + sin45°) = μ₀i√2/(2πa). The two sides of branch ABC produce field in one direction, while the two sides of branch ADC produce field in the opposite direction. H…