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?
I used j = I/A, the definition of current density: current per unit cross sectional area.
the formula for the area of a circle and for a cylinder
The Attempt at a Solution
First I tried to do the cross sectional area (a circle) times the current density, but I got none of the answer that were displayed, and by just using a circle, I'm only finding the current for a small section of the wire. So I found the area of a cylinder.
A = 2*pi*R*L (L is the length of the cylinder, not given in the problem)
j = kr
so A*j = 2*pi*R*L*k*r
if you set L and r = to R (no idea why you'd do this), then you get 2*pi*R^3*k, but the correct answer is (2*pi*k*R^3)/3?
What am I missing here, because this should be a pretty straight forward question... i think.