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(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

1

Explanation

Magnetic field at `P` is `vec(B)` , perpendicular of `OP` in the direction shown in figure.
So `vec(B)=B sin theta hat(i)-B cos theta hat(j)`

Here `H=(mu_(0))/(2pi)(I)/(r)`
`sintheta=(y)/(r)` and `cos theta=(x)/(r)`
`vec(B)=(mu_(0)I)/(2pi).(1)/(r^(2))(yhat(i)-xhat(j))=(mu_(0)I(yhat(i)-xhat(j)))/(2pi(x^(2)+y^(2)))`