If the current density in a wire or radius R is given by J = kr, 0

Question

If the current density in a wire or radius R is given by J = kr, 0 < r < R, what is the current in the wire? A) 2πkR3/³ B) 3πkR3/² C) kR3/³ D) kR² E) kR2/²

Quizplus · Accepted Answer

The current I can be found by integrating the current density J over the cross-sectional area of the wire. The current density J = kr varies with the radius r. The differential area element in cylindrical coordinates is dA = 2πr dr. Thus, the current I is the integral of J dA from 0 to R, which gives I = ∫(0 to R) kr * 2πr dr = 2πk ∫(0 to R) r^2 dr = 2πk [r^3/3] from 0 to R = 2πkR^3/3.

If the Current Density in a Wire or Radius R