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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 co-ordinates (x,y) in the z=0 plane is :

A
μ0i(y^ix^j)2π(x2+y2)
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B
μ0i(y^i+x^j)2π(x2+y2)
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C
μ0i(y^jx^i)2π(x2+y2)
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D
μ0i(y^j+x^i)2π(x2+y2)
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Solution

## The correct option is A μ0i(y^i−x^j)2π(x2+y2)Magnetic feild at P is →B perpendicular to OP in the direction shown in the figureSo, →B=Bsinθi−Bcosθj Here, B=μ02π.Irsinθ=yrcosθ=xr→B=μ0I2π.1r2(y^i−x^j)=μ0I(y^i−x^j)2π(x2+y2)As r2=x2+y2Hence the correct answer is μ0I(y^i−x^j)2π(x2+y2)

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