A large conducting plane possesses a surface charge density of 1.0 10⁻⁴ C m ⁻² . Determine the electrostatic energy stored within a cubical volume of edge 1.0 cm situated in front of the plane.

Step-by-step solution

The electric field just outside a large conducting plane is given by: E = ₀ where is the surface charge density. The electrostatic energy density (energy stored per unit volume) in the electric field is: u = 1 2 ₀ E^2 = 1 2 ₀ ( ₀ )^2 = ^2 2 ₀ The volume of the cubical region is: V = a^3 = (1.0 10⁻² m )^3 = 1.0 10⁻⁶ m ^3 The total electrostatic energy stored in this volume is: U = u V = ^2 2 ₀ V Substituting the given values = 1.0 10⁻⁴ C m ⁻² and ₀ = 8.85 10⁻¹² F m ⁻¹ : U = (1.0 10⁻⁴)^2 2 8.85 10⁻¹² 1.0 10⁻⁶ U = 10⁻