Repeat the above problem, but with the current in both wires shown in fig. directed into the plane of the figure.
Derive the 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 direciton 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_0Ix)/(pi(x^2+a^2))`

Answer

D

Explanation

(d)
At a position on the x-axis:
`B_(n et)=2(mu_0I)/(2pir)cos theta=(mu_0I)/(pi(sqrt(x^2+a^2))) a/(sqrt(x^2+a^2))`
`B_(n et)=(mu_0Ix)/(pi(x^2+a^2))`
It's graphs is shown below.

The magnetic field is a maximum when :
`(dB)/(dx)=0=C/(x^2+a^2)-(2Cx^2)/(x^2+a^2)^2`
`(x^2+a^2)=2x^2 implies x=+-a`
When `xgt gta, B~~(mu_0I)/(pix),`
which is just like a wire carrying current 2I.