Repeat the above problem, but with the current in both wires shown in fig. directed into the plane of the figure.
Graph the magnitude of `vecB` at points on the x-axis.

Options

A.
B.
C.
D.

Answer

B

Explanation

(b)
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.