Energy Density Formula

Energy Density Formula:

Energy Density is defined as the total amount of energy in a system per unit volume. Energy density is the computation of the amount of energy that can be stored in a given mass of a substance or a system. So, the more the energy density of a system or material, the greater will be the amount of energy stored in its mass. It is denoted by the letter U. Magnetic and electric fields can also store energy.

Energy can be stored in many varieties of substances and systems. Any material can release the energy in four types of reactions. Which are nuclear, chemical, electrochemical and electrical. While calculating the amount of energy in a system most often only useful or extractable energy is measured.

Energy Density can be defined as the total amount of energy in a system per unit volume. For example, the number of calories available per gram weight of the food. Foodstuffs have low energy density and will provide less energy per gram of the food. It means that we can eat more of them due to fewer calories.

The energy density of a capacitor or an electric field is 

UE=(1 / 2)ε₀E²

Where

• UE is Electrical Energy Density
• ε₀ is Permittivity  
• E=energy density  

The energy density of a magnetic field or an inductor is 

UB=(1 / 2)μ₀B²

Where

• UB is the magnetic energy density.
• μ₀ is permeability.
•  B is Magnetic Field

The energy density of a magnetic field may be expressed as  a physical pressure, and the energy required to compress a compressed gas a little more may be determined by multiplying the difference between the gas pressure and the external pressure by the change in volume.

Solved examples:

1. Calculate the energy density of an inductor with a magnetic field of B=7 T.

Given that  B=7 T,  μ₀=4π10^-7NA^-2

Since,

UB=(1 / 2) μ₀B²

UB=(1 / (2  4π 10^-7)) 7²

UB=(1 / 25.12   10^-7)×49 

UB=1.9506 10^-7J/m³

2. Find the energy density of a capacitor if its electric field,  E=4v / m.

Given that E=4v / m.

know that,

ε₀=8.8541 10^-12

The energy density formula of the capacitor is 

U =(1 ×  8.8541 10-12 4²) / 2

U=2.83×10^-10 .