Two long parallel wires carrying currents 8 A and 15 A in opposite directions are placed at a distance of 7 cm from each other. A point P is equidistant from both the wires such that the lines joining the point P to the wires are perpendicular to each other. The magnitude of magnetic field at P i s ____ × 10⁻⁶ T. (Given √2 = 1.4)
Physics · Magnetic effect of current · biot savart law and magnetic field due to straight conductor ,arc and ring
JEE Mains 25 January 2023 Shift 2 Evening Shift

Question

Two long parallel wires carrying currents 8 A and 15 A in opposite directions are placed at a distance of 7 cm from each other. A point P is equidistant from both the wires such that the lines joining the point P to the wires are perpendicular to each other. The magnitude of magnetic field at P i s ____ × 10⁻⁶ T. (Given √2 = 1.4)

Physics · Magnetic effect of current · biot savart law and magnetic field due to straight conductor ,arc and ring

JEE Mains 25 January 2023 Shift 2 Evening Shift

G1 Physics · Accepted Answer

The geometry gives distance from P to each wire d = 7/√2 cm. The two magnetic fields at P are perpendicular. Therefore B = [μ₀/(2πd)]√(8² + 15²). Since √(8²+15²) = 17 and d = 7/(1.4) cm = 5 cm = 0.05 m, B = (2×10⁻⁷/0.05)(17) = 68 × 10⁻⁶ T.