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Q.

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

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a

μ0I(yi^xj^)2π(x2+y2)

b

μ0I(xj^yi^)2π(x2+y2)

c

μ0I(xi^yj^)2π(x2+y2)

d

μ0I(yi^+xj^)2π(x2+y2)

answer is A.

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Detailed Solution

In the z = 0 plane, the situation is as follows
 Question Image
Here,P(x,y) is the point and  r=x2+y2
Magnetic field at P is perpendicular to OP, as it is shown in figure.
 B=B  sinθi^B  cosθj^
Here,  B=μ02πIr
 sinθ=yr,cosθ=xr B=μ0I2πr(yri^xrj^)=μ02πI(yi^xj^)(x2+y2)

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