Last updated: Jan 31, 2024

Energy Density of Fields Calculator

Q: How can I calculate energy density?

The formula for the energy density of fields is u = (ε 0 /2)E 2 + 1/(2μ 0 )B 2 . To calculate it: Find the energy density for the electric field, e.g., E = 2,000 kN/C : u E = (8.8541 x 10 -12 /2)×(2 × 10 6 ) 2 = 17.71 J/m 3 . Put the value of B = 3 × 10 -2 T : u B = 1/(2 × 4π × 10 -7 )× (3 × 10 -2 ) 2 = 358.1 J/m 3 . Sum up: 17.71 J/m 3 + 358.1 J/m 3 = 17.71 J/m 3 .

Q: What is the energy density of a capacitor having the electric field 50 N/C?

Given E = 50 N/C, energy density is 1.1068 × 10 -8 J/m 3 . Use formula u = (ε 0 /2)E 2 = (8.8541 x 10 -12 /2)×(50) 2 = 1.1068 × 10 -8 J/m 3 . Note that magnetic field B = 0 . Total energy density is 1.1068 × 10 -8 + 0 = 1.1068 × 10 -8 J/m 3 .

Q: Is there a theoretical limit for energy density?

Yes , energy density determines the total amount of energy you can store in a specific volume, so you cannot add infinite amounts of energy to a finite volume . The energy density limit is proportional to the area enclosing the volume. Of the known objects, some types of stars have the highest energy density.

Q: How can we increase the energy density of a battery?

Mainly by using different battery materials that happen to have better energy density. Also, keep optimum operating temperatures and the battery in good condition by maintaining it properly. These can help to increase the amount of energy stored in a battery.

Created by Dominik Czernia, PhD

Dominik Czernia

PhD, Institute of Nuclear Physics PAN

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Physicist at the Institute of Nuclear Physics in Kraków interested in magnetism and always ready to explain everything to everyone in simple terms. He is currently working on adding more scientific papers to his collection, accompanied by his son and another baby on its way. A perfectionist with an acute eye for detail, he has a unit converter in his brain and uses it to compare prices at the supermarket. Loves peace and quiet, especially during hiking. See full profile

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Reviewed by Bogna Szyk and Steven Wooding

Steven Wooding

Physicist holding a 1st class degree and a member of the Institute of Physics. Creator of the UK vaccine queue calculator, and featured in many publications, including The Sun, Daily Mail, Express, and Independent. Tenacious in researching answers to questions and has an affection for coding. Hobbies include cycling, walking, and birdwatching. You can find him on Twitter @OmniSteve. See full profile

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Table of contents

What is energy density?Energy density equation Sources of electric and magnetic fields FAQs

Did you know that electric and magnetic fields can store a specific amount of energy? Now you can compute that energy with our energy density of fields calculator. It can be especially useful when describing electromagnetic waves — rays of light.

In the context of the physics of conductive fluids, energy density behaves like an additional pressure that adds to the gas pressure. In the text below, we have described what energy density is and how to calculate energy density in a vacuum using the energy density equation.

What is energy density?

Energy density is the amount of energy stored in a given volume (or mass) of a substance. The higher the energy density of a substance, the greater the energy it can store. There are many different types of energy stored in materials, for example: nuclear, chemical, electrochemical, or electrical.

Electric and magnetic fields can also store energy. For example:

Lithium-ion batteries store energy in the electric field for a cell phone (check our battery capacity calculator);
Every typical magnet stores energy in the magnetic field; and
The heat from an electromagnetic wave (light), where the energy is stored in oscillating electric and magnetic fields.

Energy density equation

The energy density of an electric field and magnetic field in a vacuum can be estimated with the following energy density equation:

u = \frac{\varepsilon_0}{2}\bold{E}^2 + \frac{1}{2\mu_0}\bold{B}^2

where:

$u$ — Energy density;
$\bold{E}$ — Electric field;
$\bold{B}$ — Magnetic field;
$\varepsilon_0$ — Vacuum permittivity $\varepsilon_0 \approx 8.8541 \times 10^{-12}\ \rm{F/m}$ ; and
$\mu_0$ — Vacuum permeability $\mu_0 \approx 4\pi \times 10^{-7}\ \rm{H/m}$ .

The total energy density of an electric field and magnetic field in SI units is expressed in joules per cubic meter J/m³. It means that every 1 m³ volume of substance stores 1 J of energy.

Sources of electric and magnetic fields

You can find electric and magnetic fields everywhere! We have already mentioned that sunlight consists of oscillating electric and magnetic fields.

We encourage you to check our other calculators, where we have further presented different sources of both fields in the electric field of a point charge calculator and the solenoid magnetic field calculator.

FAQs

How can I calculate energy density?

The formula for the energy density of fields is u = (ε₀/2)E²+ 1/(2μ₀)B². To calculate it:

Find the energy density for the electric field, e.g., E = 2,000 kN/C:

u_E = (8.8541 x 10^-12/2)×(2 × 10⁶)² = 17.71 J/m³.
Put the value of B = 3 × 10^-2 T:

u_B = 1/(2 × 4π × 10^-7)× (3 × 10^-2)² = 358.1 J/m³.
Sum up: 17.71 J/m³ + 358.1 J/m³ = 17.71 J/m³.

Which fuels have the highest energy density?

Uranium has the highest energy density among available fuels. Next are thorium, hydrogen, methane, liquid natural gas, and propane. The higher the energy density, the higher the fuel quality and the simpler the chemical structure. Therefore, gases are generally higher-quality fuels than wood or coal.

What is the energy density of a capacitor having the electric field 50 N/C?

Given E = 50 N/C, energy density is 1.1068 × 10^-8 J/m³.

Use formula u = (ε₀/2)E² = (8.8541 x 10^-12/2)×(50)² = 1.1068 × 10^-8 J/m³.
Note that magnetic field B = 0.
Total energy density is 1.1068 × 10^-8 + 0 = 1.1068 × 10^-8 J/m³.

Is there a theoretical limit for energy density?

Yes, energy density determines the total amount of energy you can store in a specific volume, so you cannot add infinite amounts of energy to a finite volume. The energy density limit is proportional to the area enclosing the volume. Of the known objects, some types of stars have the highest energy density.

How can we increase the energy density of a battery?

Mainly by using different battery materials that happen to have better energy density. Also, keep optimum operating temperatures and the battery in good condition by maintaining it properly. These can help to increase the amount of energy stored in a battery.