Question

A current I flows down a wire of radius a.

(a) If it is uniformly distributed over the surface, what is the surface current den- sity K?
(b) If it is distributed in such a way that the volume current density is inversely proportional to the distance from the axis, what is J(s)?

Answer 1

Part a)

`K = (I)/(\pi a^2)`

Part b)

`J(s) = (CL)/(r)`

here we know that L = length of the wire

Step-by-step explanation:

Part a)

Current density is given as

`K = (I)/(A)`

`K = (I)/(\pi a^2)`

since current is uniformly divided across the crossection of the wire so it is given as

`K = (I)/(\pi a^2)`

Part b)

As we know that volume current density is inversely proportional to the distance from the axis

So we will have

`(I)/(\pi r^2 L) = (C)/(r)`

so we have

`J(s) = (CL)/(r)`

here we know that L = length of the wire