Practicing Success
A long cylinder contains charge distributed uniformly having volume charge density ρ. |
What would be the electric field inside the cylinder if the volume charge density of the cylinder varies according to the relation ρ = kx2? |
kx2/2ε0 i kx2/4ε0 i kx3/4ε0 i kx3/2ε0 i |
kx3/4ε0 i |
$ Q_{in} = \int_0^x{\rho 2\pi lxdx} = \int_0^x{kx^2 2\pi lxdx} = \frac{k\pi l x^4}{2} $ $ \text{Using gauss law } E.2\pi xl = \frac{q_{in}}{\epsilon_0} = \frac{k\pi l x^4}{2\epsilon_0} $ $\Rightarrow E = \frac{kx^3}{4\epsilon_0}$ |