What is the current in a wire of radius R = 2.02 mm if the magnitude of the current density is given by (a) Ja = J0r/R and (b) Jb = J0(1 - r/R) in which r is the radial distance and J0 = 3.74 × 104 A/m2? (c) Which function maximizes the current density near the wire’s surface?

Explanation:

For this problem we have to take into account the expression

J = I/area = I/(π*r^(2))

By taking I we have

I = π*r^(2)*J

(a)

For Ja = J0r/R the current is not constant in the wire. Hence

and on the surface the current is

(b)

For Jb = J0(1 - r/R)

and on the surface

(c)

Ja maximizes the current density near the wire's surface

Additional point

The total current in the wire is obtained by integrating

and in a simmilar way for Jb

And it is only necessary to replace J0 and R.

I hope this is useful for you

regards