Energy Density in an Electric Field

Energy is defined as the ability to perform work. Studies have shown that it is possible to transfer energy from one medium to another and use it to perform tasks that allow the way of life to exist. Walking, cooking, driving, and other daily activities all require a definite amount of energy.

Energy Density

The amount of energy that can be deposited in a mass of a substance or a system is known as energy density. In general, a system or material with more energy density can store a greater amount of energy in its mass.

There are four types of reactions in which a material can release energy–nuclear, chemical, electrochemical, and electrical. Most times, only usable or retrievable energy is calculated when determining the total energy in a system. Energy density is frequently denoted by U in equations.

Concept of Field Energy

When the function of a battery is exciting the parallel plates capacitor, it operates, and the amount of work done in the process moves the charges apart. Now consider:

Total charge as Q; (by the motion of positive charge and negative charge separated from each other)

Here, the voltage, denoted by V, will be:

V = Q/C

C= Capacitance.

The total work done by the battery here can be expressed as:

W= 1/2CV2

Here, the energy stored in the battery is transferred into the capacitor.

Now we need to understand where exactly the mentioned energy is stored:

We can assume this energy to have been trapped in the individual charges; which can be expressed as:

U = (½) (Q2/C)

Additionally, it can also be assumed that this energy is stored in the electric field created because of the separation of positive and negative charges.

U= (½) (CV2)

The electric field’s energy density depends on the area (A) and space (D) between charges. Consider this:

V=Ed (potential difference)

C= E 0 A/D (capacitance)

Derivation of the same:

U = 1/2 E 0E2(A*D)

Here:

1/2 E 0E2– As mentioned, this calculates the energy density/volume

(A*D) = Mass between the charges

In the area between these charges, there will be an electric field that will be constant in nature. We will observe a zero electric charge when the area outside the mentioned space is considered.

Energy Stored in an Electric Field

The occurrence of energy in an electric field comes as a result of the reaction of excited charges in a vacuum. The presence of energy in an electric field can be thought of as potential energy resulting from applying force to the field.

The capacity of an electric field represents the amount of energy it stores. It can be obtained as a force in the region containing the charge of the insulator or dipole, as observed in a capacitor. The gap between the plates of the capacitor determines the capacitance of the electric field. As the gap decreases, the capacitance increases and vice versa. The main result of this is the possibility of high voltage in the case of high-density electricity flow.

Coulomb’s law of electrostatic force states that two equal but opposite charges are attracted to each other. These charges accelerate and collide in the centre. According to the theory, when viewed from the centre, the charges appear to be mutually drawn into the centre rather than being attracted to one another. where the centre has the appearance of a vortex hole into which the charges are sucked. This is an important concept in conventional electricity. The negative or counter-space of the electric field is represented by that hole in space. Magnetism takes up space. Electricity is both non-spatial and anti-spatial. In a more profound understanding of electricity, a general concept would be that energy is stored in counter-space.

A pressed coil spring is analogous to an electric line of force. The tension in the spring represents potential energy, which is measured in volts. A material’s capacitance is determined by how much it can be pressed into a tensed spring.

Examples of Calculations of Energy Density in Electric Field 

Energy density in an electric field can be calculated as demonstrated by the following example.

For example:

The value of an electric field in a given area is 8*107V/m. Calculate the electric density of the space.

Solution:

We know that energy density is:

UE = 1/2E0E2

E0 is given = 8.85×10−12C2N−1m−2;  (vacuum permittivity)

So, by transposing the values in the equation, we will get

UE = 1/2 ×8.85×10−12× (8×107)2

Solving the equation will get the value of 28320 joules as the energy density in the electric field.

Notes on Energy Density in an Electric Field

• A system or material with a higher energy density can store a greater amount of energy in its mass.
• Energy can be stored in a wide range of substances and systems. All materials have energy stored in various systems, such as chemical energy, electrochemical energy, and nuclear energy. These energies can be used for a variety of purposes.
• Energy density can be defined as the amount of energy per unit volume or mass or the amount of energy stored in a system, material, or region of space.
• Energy density can be expressed as energy per volume or energy per mass.
• Most times, only extractable energy is measured when calculating the amount of energy in a system.
• Energy density is frequently denoted by U in scientific equations.
• Energy is also stored in magnetic and electrical fields.
• The formula for energy density/volume when considering an electric field is:

                            UE = 1/2E0E2

• The formula for energy density/volume when considering a magnetic field is:

                            UB = B2/(2µ0)

Conclusion

Energy density is the amount of energy per unit volume or mass or the amount of energy stored in a system, material, or region of space. The concept of energy density in an electric field is of significance as it builds on the concept of potential energy and helps understand how the concept of energy density works in various models. By adding the density of electric and magnetic fields, we can calculate the total density.