Q. 435.0( 2 Votes )

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.

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,




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