Question

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

Answer 1

Answer:

The  magnetic energy density  is  $E_B = 9.95 *10^{-4} \ J/m^3$

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  

          $x = \frac{0.5 * 1*10^{-4}}{1}$

          $x = B= 5.0 *10^{-5} \ T$

Generally the magnetic energy density is  mathematically represented as

        $E_B = \frac{B^2}{ 2 * \mu_o }$

  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  

       $E_B = \frac{(5*10^{-5})^2}{ 2 * 4\pi * 10^{-7} }$

       $E_B = 9.95 *10^{-4} \ J/m^3$