Energy Density of Field Calculator, Formula, Calculation with Example

Energy Density of Field Calculator:

Enter the Electric field in kN/C, Magnetic field in mT, and you get the calculation of Energy density in J/m³

Energy Density of Fields Calculator

Energy Density Equation:

Energy Density is U(j/m3) in joules per meter3 is equal to the square electric field E2 (v/m) in volts per meter and multiply the vacuum permittivity ε0(F/m) in Farad per meter and divided by the two and addition of the square of  magnetic field B2(t) in telsa and divided by the vacuum permeability μ0(H/m) in Henry per meter and multiply the 2.Hence the Energy density formula can be written as

U(j/m3) = E2 (v/m)* (ε0(F/m) /2 ) + B2(t) / (μ0(H/m)* 2 )

E = √[[U –B2  / (μ0* 2 ) / (ε0 /2 )]

B = √[[U –E2  / (ε0* 2 ) * (μ0 /2 )]

Where,

B = magnetic field

E= electric field

U= energy density

ε0 is the vacuum permittivity ε0 = 8.8541 *10-12 F/m

μ0 is the vacuum permeability μ0 =4 π *10-7 H/m

Example:1

Calculate the energy density of the electric and magnetic fields? In a certain region of space, the magnetic field has  a value of 2.5 *10-2 T and the electric field is 8 *106 V/m.

Answer:

Given that

Electric field E =8 *106 V/m

Magnetic field B= 2.5 *10-2 T

ε0 = 8.8541 *10-12 F/m

μ0 =4 π *10-7 H/m

Energy density = U=E2 * (ε0 /2 ) + B2 / (μ0* 2 )

=(64*106) * (8.8541 *10-12 /2 ) +(2.5 *10-2)2 / (4 π *10-7 *2)

=0.0002833312 +0.000625/0.0251327

=0.000283312+0.00402123

=32.3524 j/m3

Therefore, the energy density is 32.3524 j/m3

Example:2

Calculate Magnetic field of the energy density 25 j/m3.

Answer:

U=25 j/m3

ε0 = 8.8541 *10-12 F/m

μ0 =4 π *10-7 H/m

By using formula

B= √ (u –( ε0 /2 ) * (μ0 *2 )

B= √(25 –(8.8541 *10-12 /2 ) *(4 π *10-7 *2 )

B=0.0079266telsa

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