Figure shows an end view of two long, parallel wires perpendicular to the xy plane, each carrying a current I, but in opposite directions.

Derive an expression for the magnitude of `vecB` at any point on the x-axis in terms of the x-coordinate of the point. What is the direction of `vecB`?

Options

A. `(sqrt2mu_0Ia)/(pi(x^2+a^2))`
B. `(3mu_0Ia)/(pi(x^2+a^2))`
C. `(mu_0Ia)/(2pi(x^2+a^2))`
D. `(mu_0Ia)/(pi(x^2+a^2))`

Answer

D

Explanation

(d)
At a position on the x-axis:
`B_(n et)=2(mu_0I)/(2pir)sin theta=(mu_0I)/(pi(sqrt(x^2+a^2))) a/(sqrt(x^2+a^2))`
`B_(n et)=(mu_0Ia)/(pi(x^2+a^2))`
It's graphs is shown below.

The magnetic field is a maximum at origin, `x=0`.
When `xgt gta, B~~(mu_0Ia)/(pix^2)`