Question

A charge of 0.51 C is spread uniformly throughout a 33 cm rod of radius 4 mm. What are the volume and linear charge densities

Answer 1

The definition of volumetric charge density is given as the ratio between the load per unit volume, while the linear load is the same ratio of the load but per unit length. Applying these concepts then we have that the volumetric density of charge is,

Here,

q = Charge

V = Volume

Replacing we have,

$\gamma = \frac{0.51}{\pi r^2 l}$

$\gamma = \frac{0.51}{\pi (4*10^{-3})^2(0.33)}$

$\gamma =30475.84C/m^3$

And the linear charge density is

$\rho = \frac{q}{l}$

$\rho = \frac{0.51}{0.33}$

$\rho = 1.54C/m$