Magnetics 2 Question 11

11. 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 coordinate (x,y) on the z=0 plane is

(2002, 2M)

(a) μ0I(yi^xj^)2π(x2+y2)

(b) μ0I(xi^+yj^)2π(x2+y2)

(c) μ0I(xj^yi^)2π(x2+y2)

(d) μ0I(xi^yj^)2π(x2+y2)

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Answer:

Correct Answer: 11. (a)

Solution:

  1. Magnetic field at P is B, perpendicular to OP in the direction shown in figure.

So, B=Bsinθi^Bcosθj^

Here, B=μ0I2πr

sinθ=yr and cosθ=xrB=μ0I2π1r2(yi^xi^)=μ0I(yi^xj^)2π(x2+y2)( as r2=x2+y2)



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