Electric Potential Energy

Consider an electrostatic field E due to a charge Q placed at the origin. Now, bring a test charge q from a point R to a point P against the repulsive force on it due to the charge Q. This will happen if Q and q are either positive or both negative.

 

 Take Q, q > 0. First, assume that the test charge q is so small that it does not disturb the original configuration.

Second, in bringing the charge q from R to P, apply an external force F_ext just enough to counter the repulsive electric force FE (i.e, F_ext= –F_E).

This means there is no net force on or acceleration of the charge q when it is brought from R to P, i.e., it is brought with infinitesimally slow constant speed.

Work done by the external force is the negative of the work done by the electric force, and gets fully stored in the form of potential energy of the charge q.

If the external force is removed on reaching P, the electric force will take the charge away from Q – the stored energy (potential energy) at P is used to provide kinetic energy to the charge q in such a way that the sum of the kinetic and potential energies is conserved.

Thus, work done by external forces in moving a charge q from R to P is

At every point in electric field, a particle with charge q possesses a certain electrostatic potential energy, this work done increases its potential energy by an amount equal to potential energy difference between points R and P.

Thus, potential energy difference

 (Note here that this displacement is in an opposite sense to the electric force and hence work done by electric field is negative, i.e., –W_RP.) 

Therefore, can define electric potential energy difference between two points as the work required to be done by an external force in moving (without accelerating) charge q from one point to another for electric field of any arbitrary charge configuration.

  

Two important comments may be made at this stage:

(i) Work done by an electrostatic field in moving a charge from one point to another depends only on the initial and the final points and is independent of the path taken to go from one point to the other. This is the fundamental characteristic of a conservative force.

  

(ii) A convenient choice is to have electrostatic potential energy zero at infinity. With this choice, if take the point R at infinity,

 Potential energy of charge q at a point (in the presence of field due to any charge configuration) is the work done by the external force (equal and opposite to the electric force) in bringing the charge q from infinity to that point.

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Some of these questions which may be asked in your Board Examination 2012-2013

Q1: When a plastic comb is passed through dry hair, what type of charge is acquire by comb?

Q2: Does motion of a body affect its charge?

Q3: What is the origin of frictional forces?

Answer these questions in comment box and help your friends