A large conducting plane has a surface charge density 1.0 × 10 –4 C m –2 . Find the electrostatic energy stored in a cubical volume of edge 1.0 cm in front of the plane.

Question

Philoid · Accepted Answer

Given,

Surface charge density,σ1.0 × 10^–4 C m^–2

Edge length of the cube, e=1.0 cm=0.01m

Permittivity of free space, ε₀= 8.85×10^-12 F/m

Formula used

For a conducting plate infinite length), the electric field, E is,

And the electrostatic energy density or the energy per volume is,

Substituting eqn.1 in eqn.2 will result in,

Now the energy stored in volume V is

In the problem, we have to find the force inside a cube of edge e length.

So, we replace V with e³ in eqn.3

So,

Now, substituting the known values in the above equation, it becomes,

Or,

A large conducting plane has a surface charge density 1.0 × 10–4 C m–2. Find the electrostatic energy stored in a cubical volume of edge 1.0 cm in front of the plane.

A large conducting plane has a surface charge density 1.0 × 10^–4 C m^–2. Find the electrostatic energy stored in a cubical volume of edge 1.0 cm in front of the plane.