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Question

A long straight wire along the Z-axis carries a current I in the negative Z−direction. The magnetic vector field →B at a point having coordinates (x,y) in the Z=0 plane is

A
μ0I(y^ix^j)2π(x2+y2)
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B
μ0I(x^iy^j)2π(x2+y2)
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C
μ0I(x^i+y^j)2π(x2+y2)
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D
μ0I(x^iyx^j)2π(x2+y2)
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Solution

The correct option is A μ0I(y^i−x^j)2π(x2+y2)The wire carries a current I in the negative z−direction.We have to consider the magnetic vector field →B at (x,y) in the z=0 plane.Magnetic field →B is perpendicular to OP.∴→B=Bsinθ^i−Bcosθ^jsinθ=yr,cosθ=xrB=μ0I2πr∴→B=μ0I2πr2(y^i−x^j)or →B=μ0I(y^i−x^j)2π(x2+y2).

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