A region of space contains a magnetic field of 500 G and an electric field of
3 *10⁶ N/C. The magnetic energy density in a cubical box of side = 20 cm in this region is

Question

A region of space contains a magnetic field of 500 G and an electric field of 3 *10⁶ N/C. The magnetic energy density in a cubical box of side = 20 cm in this region is

Quizplus · Accepted Answer

The magnetic energy density (um) can be calculated using the formula:
um = (B^2) / (2*μ0)
where B is the magnitude of magnetic field and μ0 is the permeability of free space.

In this case, B = 500 G = 500 x 10^-4 T
and μ0 = 4π x 10^-7 T m/A

Substituting the values, we get:
um = (500 x 10^-4)^2 / (2 x 4π x 10^-7) = 995 J/m^3

The volume of the cubical box is:
V = (0.20 m)^3 = 8 x 10^-3 m^3

Therefore, the total magnetic energy in the box is:
Um = um x V = 995 x 8 x 10^-3 = 7.96 J

Hence, the magnetic energy density in the given region is 995 J/m^3, and the correct answer is option D.

A Region of Space Contains a Magnetic Field of 500