# Volume Charge Density Formula

In electromagnetism, the charge density tells how much charge is present in a given length, area or volume. The greek symbol Pho $\left(\rho\right)$  denotes electric charge, and the subscript V indicates the volume charge density.

The charge in terms of volume charge density is expressed as,

$\huge q=int\, \rho\, dv$

Where,
$\rho$ is charge density,
dv is change in volume.

The formula can also be written in a simple term as shown below.

$\huge \rho =\frac{q}{v}$

Where,
q is the charge,
v is the total volume in $m^{3}$.

### Volume Charge Density Solved Problems

Question 1: Find the volume charge density if charge of 10 C is applied across the area of $2\,m^{3}$.

Solution:

Given:
Charge q = 10 C
Volume v = $2\,m^{3}$.

The volume charge density formula is,

$\large \rho =\frac{q}{v}$

$\large \rho =\frac{10C/m}{2m^{3}}$

$\large \rho =5\,C/m^{3}$

#### Practise This Question

A circular hoop of mass m and radius R rests flat on a horizontal frictionless surface. A bullet, also of mass m and moving with a velocity v, strikes the hoop and gets embedded in it. The thickness of the hoop is much smaller than R. The angular velocity with which the system rotates after the bullet strikes the hoop is: