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Question

# 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 coordinates (x, y) in the z=0 plane is :

A
μ0I(y^ix^j)2π(x2+y2)
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B
μ0I(x^iy^j)2π(x2+y2)
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C
μ0I(x^jy^i)4π(x2+y2)
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D
μ0I(x^iy^j)4π(x2+y2)
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Solution

## The correct option is A μ0I(y^i−x^j)2π(x2+y2)An infinite wire carrying current in (−z) axiswe have →l=(−^k) (current vector)→l=x^i+y^j⇒r2=x2+y2using Biot-Savart law fo rinfinite wire→B=μ0I2πr(→l×→rr) (→l×→rr is the unit vector along →B)=μ0I2πr2[(−^k)×(x^i+y^j)]⇒→B=μ0I2π(x2+y2)(y^i−x^j) (Ans)

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