Question
Explain electric potential energy difference and discuss its important points.
✓
Answer
→As shown in the figure, consider a charge $Q$ at the origin (of the cartesian coordinate system.) At each point in the electric field of charge Q , particle having charge $q$ possesses some potential energy.
→Work needs to be done on this charge $q$, in taking it from point R (initial positionl) to point P (final position.)
→This work increase the potentical energy of $q$ which will be equal to the potential energy difference between points R and P .
→So, the potential energy difference
$\Delta U=U_P-U_R=W_{R P}$
→Here, the displacement is in the opposite direction to the electric force, hence the work done by electric force is negative $\left(- W _{ RP }\right)$, which is called electric potential energy at point $P$ with respect to point $R$.
→For the electric field of a random electric charge, the electric potential energy difference, between two points, can be defined as the work done by external force in taking the given charge $q$ from one point to the other point without acceleration.
Important points :
(1) The right hand side term of the equation $\Delta U$ $= U _{ P }- U _{ R }$ shows that the work done by the electric field to move the electric charge from one point to another in the electric field depends only on the intial position and the final position. It does not depend on the path joining them, which is a fundamental characteristic of conservative force.
(2) There is no importance of absolute value of electrostatic potential energy. It is only the difference of electrostatic potential energy that matters.
(3) If a random constant $\alpha$ is added to the potential energy at each point, it doesn't make any difference to the potential energy difference between two points. Means, it will be :
$\left( U _{ P }+\alpha\right)-\left( U _{ R }+\alpha\right)= U _{ P }- U _{ R }$
(4) For the sake of ease, the potential energy at infinite distance is taken zero. Suppose, Point $R$ is at infinity. then, $U _{ R }= U _{\infty}=0$
$\therefore W _{ RP }= W _{\infty P }= U _{ P }- U _{\infty}= U _{ P }$
(5) The potential energy of a charge $q$ at any point, is the work done by external force in bringing that charge from infinite distance to that point only.
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