### 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 Equation:

Energy Density is U_{(j/m3)} in joules per meter^{3} is equal to the square electric field E^{2} _{(v/m)} in volts per meter and multiply the vacuum permittivity ε_{0(F/m)} in Farad per meter and divided by the two and addition of the square of magnetic field B^{2}_{(t)} in telsa and divided by the vacuum permeability μ_{0(H/m)} in Henry per meter and multiply the 2.Hence the Energy density formula can be written as

U_{(j/m3) }= E^{2} _{(v/m)}* (ε_{0(F/m)} /2 ) + B^{2}_{(t)} / (μ_{0(H/m)}* 2 )

E = √[[U –B^{2 } / (μ_{0}* 2 ) / (ε_{0} /2 )]

B = √[[U –E^{2 } / (ε_{0}* 2 ) * (μ_{0} /2 )]

Where,

B = magnetic field

E= electric field

U= energy density

ε_{0} is the vacuum permittivity ε_{0 }= 8.8541 *10^{-12 }F/m

μ_{0} is the vacuum permeability μ_{0 }=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 *10^{6} V/m.

### Answer:

Given that

Electric field E =8 *10^{6} V/m

Magnetic field B= 2.5 *10^{-2} T

ε_{0 }= 8.8541 *10^{-12 }F/m

μ_{0 }=4 π *10^{-7} H/m

Energy density = U=E^{2} * (ε_{0} /2 ) + B^{2} / (μ_{0}* 2 )

=(64*10^{6}) * (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/m^{3}

Therefore, the energy density is 32.3524 j/m^{3}

### Example:2

Calculate Magnetic field of the energy density 25 j/m^{3}.

### Answer:

U=25 j/m^{3}

ε_{0 }= 8.8541 *10^{-12 }F/m

μ_{0 }=4 π *10^{-7} H/m

By using formula

B= √ (u –( ε_{0} /2 ) * (μ_{0} *2 )

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

B=0.0079266telsa