Answer:
The magnetic energy density is [tex]E_B = 9.95 *10^{-4} \ J/m^3[/tex]
Explanation:
From the question we are told that
The earths magnetic field is [tex]B = 0.5 \ Gauss[/tex]
Now
[tex]1 \ Gauss \to 1 *10^{-4} \ T[/tex]
=> [tex]0.5 \ Gauss \to x T[/tex]
So
[tex]x = \frac{0.5 * 1*10^{-4}}{1}[/tex]
[tex]x = B= 5.0 *10^{-5} \ T[/tex]
Generally the magnetic energy density is mathematically represented as
[tex]E_B = \frac{B^2}{ 2 * \mu_o }[/tex]
Here [tex]\mu_o[/tex] is the permeability of free space with a constant value
[tex]\mu_o = 4\pi * 10^{-7} N/A^2[/tex]
substituting values for equation above
[tex]E_B = \frac{(5*10^{-5})^2}{ 2 * 4\pi * 10^{-7} }[/tex]
[tex]E_B = 9.95 *10^{-4} \ J/m^3[/tex]
