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Question

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

A
μ0I2π(x^iy^jx2+y2)
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B
μ0I2π(x^i+y^jx2+y2)
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C
μ0I4π(x^jy^ix2+y2)
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D
μ0I2π(y^ix^jx2+y2)
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Solution

The correct option is D μ0I2π(y^ix^jx2+y2)

The given situation in the question is shown in the below diagram.


From the figure, we get,

r=x2+y2; sinθ=yr; cosθ=xr

We can see that, field at point P(x,y) will have two components.

The horizontal component of the field Bx is,

Bx=Bsinθ ^i=μ0I2πx2+y2(yx2+y2) ^i

Bx=μIy2π(x2+y2) ^i

The vertical component of the field By is,

By=Bcosθ(^j)=μ0I2πx2+y2(xx2+y2) (^j)

By=μIx2π(x2+y2) (^j)

The resultant field at point P(x,y) is,

B=Bx^i+By(^j)=μ0I2π(x2+y2)(y^ix^j)

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, (D) is the correct answer.

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