Two identical long conducting wires AOB and COD are perpendicular to each other, with O their common projected intersection. They carry currents I₁ and I₂. Point P is at distance d from O normal to the plane of the wires. Find the magnitude of the resultant magnetic field at P.
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Question

Two identical long conducting wires AOB and COD are perpendicular to each other, with O their common projected intersection. They carry currents I₁ and I₂. Point P is at distance d from O normal to the plane of the wires. Find the magnitude of the resultant magnetic field at P.

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G1 Physics · Accepted Answer

Step 1: Each long wire generates field at perpendicular distance d: B₁ = μ₀I₁/(2πd) and B₂ = μ₀I₂/(2πd). Step 2: By the right-hand rule, the field directions at P are mutually perpendicular for the depicted perpendicular wires. Step 3: Magnitude B = √(B₁²+B₂²) = [μ₀/(2πd)]√(I₁²+I₂²). Final answer: (D) μ₀/(2πd) × √(I₁² + I₂²).