Q43 of 94 Page 166

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.

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,




More from this chapter

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41

A point charge Q is placed at the origin. Find the electrostatic energy stored outside the sphere of radius R centred at the origin.

 42

A metal sphere of radius R is charged to a potential V.

a) Find the electrostatic energy stored in the electric field within a concentric sphere of radius 2R.


b) Show that the electrostatic field energy stored outside the sphere of radius 2R equals that stored within it.


 44

A parallel-plate capacitor having plate area 20 cm2 and separation between the plates 1.00 mm is connected to a battery of 12.0 V. The plates are pulled apart to increase the separation to 2.0 mm.

a) Calculate the charge flown through the circuit during the process.


b) How much energy is absorbed by the battery during the process?


c) Calculate the stored energy in the electric field before and after the process.


d) Using the expression for the force between the plates, find the work done by the person pulling the plates apart.


e) Show and justify that no heat is produced during this transfer of charge as the separation is increased.


 45

A capacitor having a capacitance of 100 μF is charged to a potential difference of 24V. The charging battery is disconnected and the capacitor is connected to another battery of emf 12V with the positive plate of the capacitor joined with the positive terminal of the battery.

a) Find the charges on the capacitor before and after the reconnection.


b) Find the charge flown through the 12V battery.


c) Is work done by the battery or is it done on the battery? Find its magnitude.


d) Find the decrease in electrostatic field energy.


e) Find the heat developed during the flow of charge after reconnection.