Question

If the current density in a wire or radius R is given by J-k+5,0F wire? R, what is the current in the wire?

Answer 1

I =
`R^(2)`(K+5)

Step-by-step explanation:

Given :

J = k+5

Now selecting a thin ring in the wire of radius "r" and thickness dr.

Current through the thin ring is

dI = J X 2πrdr

dI = (K+5) x 2πrdr

Now integrating we get

I =
`\int_(0)^(R) = (K+5).2\pi rdr`

I = (K+5) 2π
`\int_(0)^(R) rdr`

I = (K+5) 2π
`(R^(2))/(2)`

I =
`R^(2)`(K+5)