# Energy Density Formula

Energy Density is defined as the total amount of energy in a system per unit volume. For example, the number of calories per gram of food. Foodstuffs that has low energy density provide less energy per gram of food which means that you can eat more of them since there are fewer calories.

It is denoted by letter U.

Magnetic and electric fields can also store energy.

In the case of the electric field or capacitor, the energy density formula is given by

$U=\frac{1}{2}\epsilon&space;_{0}E^{2}$

E = E is the electric field

ε0 = permittivity of free space

The energy density formula in case of magnetic field or inductor is given by,

$U=\frac{1}{2\mu&space;_{0}}B^{2}$

B =Magnetic field

μ =permeability of free space

Regarding electromagnetic waves, both magnetic and electric field are equally involved in contributing to energy density. Therefore, the formula of energy density is the sum of the energy density of the electric and magnetic field.

Example 1:

Find the energy density of a capacitor if its electric field,  E = 5 V/m.

Solution:

Given,

E = 5V/m

We know that,

ϵ0 = 8.8541× 10−12F/m

The energy density formula of the capacitor is given by

$U=\frac{1}{2}\epsilon&space;_{0}E^{2}$

= (1 × 8.8541×10−12×52 )/2

U= 1.10×10−10 FV2/m3

Example 2:

Find the energy density of an inductor whose magnetic field is 0.7T.

Solution

Given,

B = 0.5T

We know that,

μ = 1.25×10−6  NA-2

Energy density formula for inductor is given as,

U ={ 1 / 2$\mu _{0}$}*B2

U = [×1.25×10−60.52  ] /2

U = 9.947×104 A2T/N