How to Calculate Energy Density

Energy density is the quantity of energy stored in a region per unit volume. It is a useful measurement when dealing with electric and magnetic fields. The idea is also used in nutritional research, though the calculation in this discipline is known as caloric density. The value is a useful parameter especially when comparing different fuels. For example, hydrogen fuel has lower energy density than gasoline. A higher energy density indicates that more energy can be stored or transported for the same amount of mass.

Things You'll Need

• Calculator

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Instructions

• 1

  Write down the formula for deriving energy density "D," which is as follows: D = E ÷ V, where "E" is the total energy of the system, and "V" is the volume of the system you are working with. For example, if you wanted to calculate the energy density of a magnetic field emitted from a coil of wire forming a conductor, then you'll have to consider the energy of the magnetic field and volume the solenoid takes up.

• 2

  Find the total energy "E" of the arrangement where E = kinetic energy + potential energy. This value will depend on what type of system you are considering. For our example of the solenoid, the kinetic energy will be zero and the potential energy created from the magnetic field is: power x change in time = ½ x L x I², where "L" is the inductance along the coil of wire and "I" is the current along the wire. The total energy of the system would then equal E= 0 + ½ x L x I²= ½ x L x I².

• 3

  Derive a formula for the volume of the system. For our example, the system's shape is solenoid and the volume of a solenoid is comparable to the volume of a cylinder that is V = A x l. The symbol "A" is the cross sectional area of the cylinder formed by the solenoid and "l" is the length of the cylinder.

• 4

  Plug your values into the energy density equation and simplify it. For a magnetic field L = (µ x N² x A) ÷ l and I = (B x l)÷ (µ x N), so the energy density equation for the magnetic field would simplify to be E = (1/2 x B²)/µ. The symbol µ is is the permeability of free space or magnetic constant equaling .000001256 N/A² in SI units and "B" is the amount of magnetic flux density the field generates.

• 5

  Solve the energy density equation you derived using a calculator. For example, if the magnetic flux density generated by the solenoid is 30 N/Am Newtons ÷ (Ampers x meters) or 30 T, Teslas than the energy density for the magnetic field would be E = (1/2 x B²) ÷ µ = [½ x (30 N/Am)²] ÷ .000001256 N/A² = 35.8 N/m².