Question

if the current density in a wire is given by j=alpha*r,where alpha is a constant and r is the distance from the center of the wire, 0

Answer 1

Given:

The current density is,

`J=ar`

a is a constant, and the radius of the wire is R.

To find:

The current in the wire

Step-by-step explanation:

The current in the wire is,

`\begin{gathered} I=\int JdA \\ =\int ardA \end{gathered}`

We know,

`\begin{gathered} A=\pi r^2 \\ dA=2\pi rdr \end{gathered}`

So,

`\begin{gathered} I=\int_0^Rar*2\pi rdr \\ =2\pi a\int_0^Rr^2dr \\ =2\pi a*(R^3)/(3) \end{gathered}`

Hence, the required current is,

`(2\pi aR^3)/(3)`