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Question
A large conducting plane has a surface charge density `1.0 xx 10^-4 "Cm"^-2` . Find the electrostatic energy stored in a cubical volume of edge 1⋅0 cm in front of the plane.
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Solution
Given,
Surface charge density of the plane, `σ = 1.0 xx 10^-4 C/m^2`
Volume of the cube, `V = a^3 = 10^-6 "m"^3`
Electric field near the charged conducting plane is given as , `E = σ/∈_0` .... (i)
Energy density of electric filed,
`u = 1/2∈_0E^2`
⇒ `u = 1/2∈_0(σ/∈_0)^2`
⇒ `u = 1/2 σ^2/∈_0`
⇒ `u = 1/2 xx (1.0 xx 10^-4)^2/(8.85 xx 10^-12)`
⇒ `u = 0.056 xx 10^4 j/m^3`
`Volume = 10^-6 "m"^3`
⇒ `U = u xx V`
⇒ `U = 0.056 xx 10^4 xx 10^-6`
⇒ `U = 5.6 xx 10^-4 J`
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