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

Options

A. `(mu_(0)I(yhati-xhatj))/(2pi(x^(2)+y^(2))`
B. `(mu_(0)I(xhati+yhatj))/(2pi(x^(2)+y^(2))`
C. `(mu_(0)I(xhati-yhatj))/(2pi(x^(2)+y^(2))`
D. `(mu_(0)I(xhati-yhatj))/(2pi(x^(2)+y^(2))`

Answer

A

Explanation

`r=sqrt(x^(2)+y^(2))`
Magnetic field at `P`
`B=(mu_(0)I)/(2pir), bot^(ar)` to `OP` at `P`
as shown
`vec(B)_(P)=B_(x)hati-B_(y)hatj=B sin thetahati-B cos theta hatj`
`=By/rhati-Bx/r hatj`
`=B/r(yhati-x hatj)`
`=(mu_(0)I)/(2pir^(2))(yi-xj)`
`=(mu_(0)I)/(2pi(y^(2)+x^(2)))(yi-xj)`