Energy Density of Fields Calculator
Make use of the online Energy Density of Fields Calculator tool to calculate the energy density value effortlessly. You have to enter the electric field, magnetic field values in the fields of the calculator and click the calculate button to avail the result in a less amount of time.
Step by Step Process to Compute Energy Density
These are the simple steps to evaluate the energy density of fluids easily.
- Get the electric field, and magnetic field values
- Find the sqaure of the electric field and multiply it by the half of the vaccum permittivity constant.
- Divide the sqaure of the magnetic field by the double of the vaccum permeability constant.
- Add those two result to check the energy density value.
Energy Density Equation
Energy density is the amount of energy stored in a mass of a substance. We have different types of energy stored in materials like nuclear energy, chemical, electrical and so on. Both electric fields and magnetic fields can also store energy.
The energy density of fields in a vaccum formula is along the lines
U = E² * (ϵ₀ / 2) + B² / (μ₀ * 2)
E = √[[U - B² / (μ₀ * 2)]/(ϵ₀ / 2)]
B = √[[U - E² * (ϵ₀ / 2)] x (μ₀ * 2)]
Where,
B is the magnetic field
E is the electric field
U is the energy density
ϵ₀ is the vacuum permittivity ϵ₀ = 8.8541 x 10-12 F/m
μ₀ is the vaccum permeability μ₀ = 4π x 10-7 H/m
Example
Question: In a certain region of space, the magnetic field has a value of 1.5 x 10-2 T and the electric field is 2 x 106 V/m. Find the combined energy density of the electric and magnetic fields?
Solution:
Given that
Electric field E = 2 x 106 V/m
magnetic field B = 1.5 x 10-2 T
Energy density U = E² * (ϵ₀ / 2) + B² / (μ₀ * 2)
U = (2 x 106)² * (8.8541 x 10-12 / 2) + (1.5 x 10-2)² / (4π x 10-7 * 2)
= 4 x 1012 * 4.42705 x 10-12 + (2.25 x 10-4/(8π x 10-7)
= 17.7082 + 8.95 x 10-9
= 17.717 J/m3
Therefore, the energy density is 17.717 J/m3
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Frequently Asked Questions on Energy Density of Fields Calculator
1. How to solve the energy density of a field?
The energy density of field problems can be solved by using the equation U = E² * (ϵ₀ / 2) + B² / (μ₀ * 2), Here E, B are the electric field, magnetic field. Put the values in the equation and solve to obtain the energy density of fields.
2. What is energy density?
The energy density is defined as the total amount of energy collected in a system per unit volume. The electric and magnetic fields are the main sources for storing energy.
3. What is the unit of the energy density?
The SI unit of energy density is J/m3
4. Find the energy density of a capacitor having the electric field E = 5 V/m.
Given that,
Electric field E = 5 V/m
The energy density formula is U = 1/2(ϵ₀E2)
= 1/2(8.8541 x 10-12 x 52)
= (4.42705 x 10-12 x 25)
= 110.67625 x 10-12
Therefore, the energy density of the capacitor is 110.67 x 10-12
