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 coordinnates (x, y) in the z = 0 plane is

Options

A. `(mu_(0)I(yhat(i)-xhat(j)))/(2pi(x^(2) + Y^(2)))`
B. `(mu_(0)I(xhat(i)+yhat(j)))/(2pi(x^(2) + Y^(2)))`
C. `(mu_(0)I(xhat(j)-yhat(i)))/(2pi(x^(2) + Y^(2)))`
D. `(mu_(0)I(xhat(i)-yhat(j)))/(2pi(x^(2) + Y^(2)))`

Answer

A

Explanation

`[B] = (mu_(0))/(2pi) (i)/(sqrt(x^(2) + y^(2)))`
unit vector perpendicular to the position vector is `(yhat(i) - xhat(j))/(sqrt(x^(2) + y^(2)))`
`vec(B) = (mu_(0)i)/(2pi(x^(2) + y^(2)))(yhat(i) - xhat(j))`