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Question

A long straight wire along the z - axis carries a current i in the negative z - direction. The magnetic field B at a point having co - ordinate (x, y) on the z = 0 plane is
  1. μ0I(x^iy^j)2π(x2+y2)
  2. μ0I(x^jy^i)2π(x2+y2)
  3. μ0I(y^ix^j)2π(x2+y2)
  4. μ0I(x^i+y^j)2π(x2+y2)


Solution

The correct option is C μ0I(y^ix^j)2π(x2+y2)
Magnetic field at P is B, perpendicular to OP in direction shown in figure.

So, B=B sin θ ^iB cos θ^j
Here, B=μ0I2πr
sin θ=yrandcosθ=xr
B=μ0I2π.1r2(y^ix^i)=μ0I(y^ix^j)2π(x2+y2)
                                       (as r2=x2+y2)

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