Figure shows a current-carrying square loop ABCD of edge length ‘a’ lying in a plane. If the resistance of the path ABC is r and the path ADC is 2r, find the magnitude of the resultant magnetic field at the centre of the square loop.
🧲 Magnetic Field at Centre of Square Loop with Unequal Resistance | JEE Concept 📌 Question: Figure shows a current-carrying square loop ABCD of edge length ‘a’ lying in a plane. If the resistance of the path ABC is r and the path ADC is 2r, find the magnitude of the resultant magnetic field at the centre of the square loop. 🖼️ Question Image: 💡 Concept Used: Unequal resistance in different paths means current divides unequally in branches. Use current division rule and Biot-Savart Law or symmetry to find net magnetic field at center. Magnetic field due to a straight segment at center of square is: B = μ 0 I 4 π R ⋅ 2 sin ( θ / 2 ) or use full loop formula if current is symmetrical. 🧠 Approach: Let total current be I. Since resistances are in parallel: Current in ABC: I 1 = 2 3 I I_1 = \frac{2}{3}I I 1 = 3 2 I Current in ADC: I 2 = 1 3 I I_2 = \frac{1}{3}I I 2 = 3 1 I Both paths form half-loops and contribute to B at center ....