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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,

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

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

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

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

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 $2\,m^{3}$.


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

The volume charge density formula is,

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

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

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

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