Question

The Earth's magnetic field is approximately 0.5 Gauss. What is the magnetic energy density of this field

Answer 1

The magnetic energy density is
`E_B = 9.95 *10^(-4) \ J/m^3`

Step-by-step explanation:

From the question we are told that

The earths magnetic field is
`B = 0.5 \ Gauss`

Now

`1 \ Gauss \to 1 *10^(-4) \ T`

=>
`0.5 \ Gauss \to x T`

So

`x = (0.5 * 1*10^(-4))/(1)`

`x = B= 5.0 *10^(-5) \ T`

Generally the magnetic energy density is mathematically represented as

`E_B = (B^2)/( 2 * \mu_o )`

Here
`\mu_o` is the permeability of free space with a constant value

`\mu_o = 4\pi * 10^(-7) N/A^2`

substituting values for equation above

`E_B = ((5*10^(-5))^2)/( 2 * 4\pi * 10^(-7) )`

`E_B = 9.95 *10^(-4) \ J/m^3`