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Two identical long conducting wires AOB and COD are placed at right angle to each other, with one above other such that 'O' is their common point for the two. The wires carry I₁ and I₂ currents respectively. Point 'P' is lying at a distance 'd' from 'O' along a direction perpendicular to the plane containing the wires. The magnetic field at the point 'P' will be:
- μ₀ / (2πd) (I₁ / I₂)
- μ₀ / (2πd) (I₁ + I₂)
- μ₀ / (2πd) (I₁² - I₂²)
- μ₀ / (2πd) (I₁² + I₂²)^(1/2)
Correct answer: μ₀ / (2πd) (I₁² + I₂²)^(1/2)
Solution
The magnetic field at point P due to each wire is perpendicular to the plane of the wire and follows the right-hand rule. Since the wires are perpendicular to each other, the magnetic fields due to the two wires are perpendicular as well. The net magnetic field is the vector sum of the two fields, which results in the magnitude being the square root of the sum of the squares of the individual fields.
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