Question

Q 26.12: Assume current flows in a cylindrical conductor in such a way that the current density increases linearly with radius, from zero at the center to 1.0 A/m2 at the surface of the conductor. If the conductor has a cross sectional area of 1.0 m2, what can you say about the current in this conductor

Answer 1

The current is 0.67 A.

Step-by-step explanation:

Density, J = 1 A/m^2

Area, A = 1 m^2

Let the radius is r. And outer is R.

Use the formula of current density

`I = \int J dA = \int J 2\pi r dr\\\\I = \int_(0)^(R)(2\pi r^2)/(R) dr\\\\I = (2 \pi R^2)/(3).... (1)Now A = \pi R^2\\\\1 =\pi R^2\\\\R^2 = (1)/(\pi)\\\\So, \\\\I = (2\pi)/(3)* (1)/(\pi)\\\\I = 0.67 A`