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A long straight wire along the z- axis c...

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

A

`(mu_(0)I)/(2pi) (yhati -xhatj)/((x^(2) +y^(2)))`

B

`(mu_(0)I)/(2pi) (xhati + yhatj)/((x^(2) +y^(2)))`

C

`(mu_(0)I)/(2pi) (xhatj - yhati)/((x^(2) +y^(2)))`

D

`(mu_(0)I)/(2pi) (xhati - yhatj)/((x^(2) +y^(2)))`

Text Solution

Verified by Experts

The correct Answer is:
`A`
`oversetrarrOP = xhati + yhatj`
`hatB = (yhati -xhatj)/sqrt(x^(2) +y^(2))`
`B =(mu_(0))/(4pi) (2I)/(sqrt(x^(2) +y^(2)))`
`oversetrarrB = (mu_(0))/(4pi) (2I)/(sqrt(x^(2) +y^(2))) (yhati -xhatj)/(sqrt(x^(2) +y^(2)))`
`=(mu_(0)I)/(2pi) ((yhati -xhati))/((x^(2)+y^(2))`
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