# Electric potential energy

Jun 17th, 2015
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Introduction• We already have an introduction of work and energy while studying mechanics.• We know that central forces are conservative in nature i.e., work done on any particle moving under the influence of consrevative forces does not depend on path taken by the particle but depends on initial and final positions of the particle.

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IntroductionWe already have an introduction of work and energy while studying mechanics.We know that central forces are conservative in nature i.e., work done on any particle moving under the influence of consrevative forces does not depend on path taken by the particle but depends on initial and final positions of the particle.Electrostatic force given by Coulumb's law is also a central force like gravitational force and is conservative in nature.For conservative forces, work done on particle undergoing displacement can be expressed in terms of potential energy function.In this chapter we will apply work and energy considerations to the electric field and would develop the concept of electric potential energy and electric potential.2. Electric potential energyConside a system of two point charges in which positive test charge q' moves in the field produced by stationary point charge q shown below in the figure.Charge q is fixed at point P and is displaced from point R to S along a radial line PRS shown in the figure.Let r1be the distance between points P and R and r2be the distance between P and S.Magnitude of force on positive test charge as given by Coulumb's law isIf q' moves towards S through a small displacement drthen work done by this force in making the small displacement drisdW=FdrTotal work done by this force as test charge moves from point R to S i.e., from r1to r2is,orThus for this particular path work done

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