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

Quizplus · Accepted Answer

The energy density in electrostatics is given by u = 1/2 * ε0 * E^2, where ε0 is the permittivity of free space and E is the electric field strength. 
Substituting the given values, we get:
u = 1/2 * 8.85e-12 * (3e10)**2
u = 39.8 J/m^3
The volume of the cubical box is (0.2 m)^3 = 0.008 m^3. 
Therefore, the total electrical energy in the box is:
U = u * V = 39.8 * 0.008 = 0.318 J
Dividing this by the surface area of the box (6*0.2^2), we get:
Energy density = U / A = 0.318 / 0.24 = 1.325 J/m^2
Rounding off to the nearest 0.1 J/m^3, we get the final answer as 39.8 J/m^3.

A Region of Space Contains a Magnetic Field of 500