Physics GRE - #32

As shown below, a coaxial cable having radii $a$, $b$, and $c$ carries equal and opposite currents of magnitude $i$ on the inner and outer conductors. What is the magnitude of the magnetic induction at a point $P$ outside the cable at a distance $r$ from the axis?

1. $0$
2. $\dfrac{\mu_0 ir}{2\pi a^2}$
3. $\dfrac{\mu_0 i}{2\pi r}$
4. $\dfrac{\mu_0 i}{2\pi r}\dfrac{c^2-r^2}{c^2-b^2}$
5. $\dfrac{\mu_0 i}{2\pi r}\dfrac{r^2-b^2}{c^2-b^2}$

Solution :

Choice 1 is the answer.

The currents cancel out the magnetic fields created by each other, resulting in a net field of zero. More formally, this is an application of Ampere's Law.