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

At what value of x, the magnitude of `vecB` is maxismum?

Options

A. `x=0`
B. `x=sqrt2a`
C. `x=1//sqrt2a`
D. `x=a//2`

Answer

A

Explanation

(a)
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)`