Question

what may the equation for total energy density?

Answer 1



 



ENERGY DENSITY FORMULA

Energy Density is defined as the total amount of energy in a system per unit volume. For example, the amount of calories per gram of food. Food stuffs that has low energy density provide less energy per gram of food which means that you can eat more of them since there are fewer calories.

 It is denoted by letter U.

Magnetic and electric fields can also store the energy.

In case of electric field or capacitor, the energy density formula is given by



The energy density formula in case of magnetic field or inductor is given by,



Regarding electromagnetic waves, both magnetic and electric field are equally involved in contributing to energy density. Therefore, the formula of energy density is the sum of the energy density of electric and magnetic field.

Example 1:

Find  the energy density of a capacitor if its electric field,  E = 5 V/m.

Solution:

Given,

E = 5V/m

We know that,

ϵ0 = 8.8541×10−12 F/m

The energy density formula of capacitor is given by

 U = 1 / 2 ϵ0E2

    = 1 / 2 × 8.8541×10−12×52

    = 1.10×10−10 FV2/m3

Example 2:

Find the energy density of an inductor whose magnetic field is 0.7T.

Solution

Given,

B = 0.5T

We know that,

μ0= 4π×10−7π  NA-2

Energy density formula for inductor is given as,

U = 1 / 2μ0B2

U = 1 / 2×4π×10−7×0.52

   = 9.947×104 A2T/N