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 isμ0I(x^i−y^j)2π(x2+y2)μ0I(x^j−y^i)2π(x2+y2)μ0I(y^i−x^j)2π(x2+y2)μ0I(x^i+y^j)2π(x2+y2)

Solution

The correct option is C μ0I(y^i−x^j)2π(x2+y2)Magnetic field at P is →B, perpendicular to OP in direction shown in figure. So, →B=B sin θ ^i−B cos θ^j Here, B=μ0I2πr sin θ=yrandcosθ=xr ∴→B=μ0I2π.1r2(y^i−x^i)=μ0I(y^i−x^j)2π(x2+y2)                                        (as r2=x2+y2)

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