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The magnitude of magnetic flux density (B) at a point having normal distance d meters from an infinitely extended wire carrying current of I A is μ₀ I/(2πd) (in SI units). An infinitely extended wire is laid along the x-axis and is carrying current of 4 A in the +ve x direction. Another infinitely extended wire is laid along the y-axis and is carrying 2 A current in the +ve y direction. μ₀ is permeability of free space. Assume î, ĵ, k̂ to be unit vectors along x, y and z axes respectively. Assuming right handed coordinate system, magnetic field intensity, H at coordinate (2,1,0) will be

1. 3/(2π) k̂ weber/m²
2. 4/(3π) î A/m
3. 3/(2π) k̂ A/m
4. 0 A/m

Correct answer: 3/(2π) k̂ A/m

Solution

The magnetic field intensity H at a point in space due to multiple currents can be determined using the superposition principle. For the given currents, the contributions from each wire at the specified coordinates combine to yield a resultant magnetic field in the z-direction, specifically resulting in the value of 3/(2π) k A/m.

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