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Energy density is referred to as the calculation of the amount of energy that may be stored in a given mass of a substance or system. As a result, the higher the energy density of a system or material, the more energy is stored in its mass. Energy may be stored in a wide variety of substances and systems.
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Key Takeaways: Energy density, Energy, Density, Volume, Magnetic Field, Electric field
What is energy density?
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The total quantity of energy in a system per unit volume is known as energy density. The number of calories provided per gramme of food, for example. Foods have a low energy density, meaning they deliver less energy per gramme. Because there are less calories, we can consume more of them.
As a result, energy density can be defined as the quantity of energy accumulated in a system per unit volume. The letter U is used to represent it. Magnetic and electric fields are also important sources of energy storage.
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Energy Density Formula
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The energy density of an electric field or a capacitor is given by
U=1ε0E2/2
In the case of a magnetic field or an inductor, the energy density is given by,
U=1B2/2μ0
Both magnetic and electric fields contribute equally to the energy density of electromagnetic waves. As a result, the energy density of electric and magnetic fields is equal to the total of their energies.
U=1ε0E2/2 + 1B2/2μ0
Where,
E= electric field
ε0 = permittivity of free space
B = magnetic field
μ0 = permeability of free space
Things to Remember
- Nuclear, chemical, electrochemical, and electrical reactions are four types of reactions that can release energy from any material.
- In most cases, only usable or extractable energy is assessed when estimating the quantity of energy in a system.
- In the case of electromagnetic waves, both magnetic and electric fields contribute equally to energy density.
- The energy density formula will equal the total of the energy density of both electric and magnetic fields.
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Sample Questions
Ques: If the electric field of a capacitor is E = 5 V/m, calculate its energy density. (3 marks)
Ans: Given,
E = 5V/m
ε0 = 8.8541× 10-12F/m
The energy density formula is given as,
U=1ε0E2/2
U = 1 × 8.8541×10-12 × 52 / 2
U = 1.10×10-10FV2/m3
Ques: If the electric field of a capacitor is E = 4 V/m, calculate its energy density. (3 marks)
Ans: Given,
E = 4V/m
ε0 = 8.8541× 10-12F/m
The energy density formula is given as,
U=1ε0E2/2
U = 1 × 8.8541×10-12 × 42 / 2
U = 0.7×10-10FV2/m3
Ques: If the electric field of a capacitor is E = 20 V/m, calculate its energy density. (3 marks)
Ans: Given,
E = 20V/m
ε0 = 8.8541× 10-12F/m
The energy density formula is given as,
U=1ε0E2/2
U = 1 × 8.8541×10-12 × 202 / 2
U = 1.7×10-9FV2/m3
Ques: If the electric field of a capacitor is E = 10 V/m, calculate its energy density. (3 marks)
Ans: Given,
E = 10V/m
ε0 = 8.8541× 10-12F/m
The energy density formula is given as,
U=1ε0E2/2
U = 1 × 8.8541×10-12 × 102 / 2
U = 4.4×10-10FV2/m3
Ques: The magnetic field has a value of 3×10-2T in a certain region of space. The electric field, on the other hand, has a value of 9×10-7V/m. Calculate the total energy density of both the electric and magnetic fields. (3 marks)
Ans: Given,
B = 3×10-2T
E = 9×10-7V/m
ε0 = 8.8541× 10-12F/m
μ0 = 4π× 10-7 NA-2
U=1ε0E2/2 + 1B2/2μ0
U = (8.8541× 10-12 ×10-8×10-8)/2 + (3×10-2×3×10-2)/ 2×4π× 10-7
Total energy density U = 35842.5 + 358.1= 36200.6J/m3
Ques: The magnetic field has a value of 3×10-2T in a certain region of space. The electric field, on the other hand, has a value of 3×10-7V/m. Calculate the total energy density of both the electric and magnetic fields. (3 marks)
Ans: Given,
B = 3×10-2T
E = 3×10-7V/m
ε0 = 8.8541× 10-12F/m
μ0 = 4π× 10-7 NA-2
U=1ε0E2/2 + 1B2/2μ0
U = (8.8541× 10-12 ×10-8×10-8)/2 + (3×10-2×3×10-2)/ 2×4π× 10-7
Total energy density U = 3982.5 + 358.1 = 4340.6J/m3
Ques: The magnetic field has a value of 2×10-2T in a certain region of space. The electric field, on the other hand, has a value of2×10-7V/m. Calculate the total energy density of both the electric and magnetic fields. (3 marks)
Ans: Given,
B = 2×10-2T
E = 2×10-2V/m
ε0 = 8.8541× 10-12F/m
μ0 = 4π× 10-7 NA-2
U=1ε0E2/2 + 1B2/2μ0
U = (8.8541× 10-12 ×10-8×10-8)/2 + (2×10-2×2×10-2)/ 2×4π× 10-7
Total energy density U = 1770+ 159.1 = 1929.1J/m3
Ques: The magnetic field has a value of 10-2T in a certain region of space. The electric field, on the other hand, has a value of 10-7V/m. Calculate the total energy density of both the electric and magnetic fields. (3 marks)
Ans: Given,
B =10-2T
E = 10-8V/m
ε0 = 8.8541× 10-12F/m
μ0 = 4π× 10-7 NA-2
U=1ε0E2/2 + 1B2/2μ0
U = (8.8541× 10-12 ×10-8×10-8)/2 + (10-2×10-2)/ 2×4π× 10-7
Total energy density U = 442.7 + 39.7 = 482.4J/m3
Ques: The magnetic field has a value of 10-3T in a certain region of space. The electric field, on the other hand, has a value of 10-8V/m. Calculate the total energy density of both the electric and magnetic fields. (3 marks)
Ans: Given,
B =10-3T
E = 10-8V/m
ε0 = 8.8541× 10-12F/m
μ0 = 4π× 10-7 NA-2
U=1ε0E2/2 + 1B2/2μ0
U = (8.8541× 10-12 ×10-8×10-8)/2 + (10-3×10-3)/ 2×4π× 10-7
Ques: The magnetic field has a value of 10-1T in a certain region of space. The electric field, on the other hand, has a value of 10-8V/m. Calculate the total energy density of both the electric and magnetic fields. (3 marks)
Ans: Given,
B =10-1T
E = 10-8V/m
ε0 = 8.8541× 10-12F/m
μ0 = 4π× 10-7 NA-2
U=1ε0E2/2 + 1B2/2μ0
U = (8.8541× 10-12 ×10-8×10-8)/2 + (10-1×10-1)/ 2×4π× 10-7
Total energy density U = 44270.5+3978.8= 48249.3 J/m3
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