Question

In a coaxial, straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. Where the magnetic field will be zero?
(A). outside the cable
(B). inside the inner conductor
(C). inside the outer conductor
(D). in between the two conductors

Answer 1

Here we are using biot- savart law. And to calculate the magnetic field we are considering an ampere loop around the cable.

Complete step by step answer:
In a coaxial cable, there are two cables, one inside the other. The cable which lies inside is called the inner cable. The cable that covers the inner cable is known as outer cable. The currents through each coil, that is the inner coil and the outer coil will be in opposite directions. That is, in other words we can say that, if the current through the inner coil is along the upward direction, then the current through the outer coil will be along the downwards direction.

Now let us consider an ampere loop around the cable. And we know that the magnetic field in an ampere loop is calculated as, $\oint {B.dl}$. And its value is calculated as the product of magnetic permeability and the current enclosed. So let us calculate the magnetic field around the loop as,
$\oint {B.dl} = {\mu _0}i$
As the cable consists of current flowing in two opposite directions, we have,
$\oint {B.dl} = {\mu _0}\left( {i - i} \right)\\\ = 0$

That means in a coaxial cable the magnetic field is zero outside the cable.

And in the other cases like, inside the inner conductor, inside the outer conductor, and in between the two conductors, the magnetic field will be a constant as the applying current is the one that passes through the inner cable only.

Thus, the correct option is (A).

Note:
When there is current flowing through two opposite directions, they flow in such a manner to nullify the other. So if one of the current is flowing upwards and one along downward, then these two nullify each other.