Electric Potential

Electric Potential due to a Point Charge Consider the electric potential due to a point charge q, As we move from point A, at distance r

_{A}from the charge q, to point B, at distance r_{B}from the charge q, thechangein electric potential isRemember, the little "caret" or "hat" over the vector

rmeans this is aunit vector-- it points in the radial direction and has a magnitude ofone.Only the

radialdistance r determines the work done or the potential. We can move through any angle we like and, as long as the radial distance remains constant, no work is done or there is no change in the electric potential.This is the change in

electric potentialdue to a point charge as we move from r_{A}to r_{B}.We could ask about the change in

electric potential energyas we move a charge q' from radius r_{A}to r_{B}due to a point charge q,As with gravitational potential energy, it is more convenient -- and, therefore, useful -- to talk about the electric potential energy or the electric potential

relative tosome reference point. We will choose that reference point to be infinity. That is,That means we can then write the electric potential at some radius r as

If we bring in a charge q', a distance r, from charge q, it (or "the system") will have electric potential energy of

Here are charges q

_{1}and q_{2}, a distance r_{12}apart. Their electric potential energy isThat is,

that much workis required to bring these two charges infrom infinitly far awayto this present distance of r_{12}apart. Think of bringing q_{1}in initially. With no other charges around, no work is required. Now, with q_{1}in place, bring in charge q_{2}from infinity to r_{12}. Theworkrequired is now stored up as electric potential energy. Of course we can talk about the "point in space" located at distance r_{12}from charge q_{1}and talk about the electric potential at thatpoint.Remember, energy is a scalar. Electric potential is a scalar.

We have equations to tell us the electric potential energy of two charges or the electric potential at a point in space because of

oneelectric charge. What if we havemore than oneelectric charge?That is, the total or net electric potential is the

scalarsum of the electric potential due to each of the individual point charges q_{i}.There are no navigational links from these Numerical Examples to get BACK to this page. You will have to use BACK or GO from your internet browser.

(c) Doug Davis, 2002; all rights reserved

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