Potential energy is closely linked with forces. If the work done moving along a path which starts and ends in the same location is zero, then the force is said to be conservative and it is possible to define a numerical value of potential associated with every point in space. A force field can be re-obtained by taking the vector gradient of the potential field. In practical terms, this means that one can set the zero of U and Φ anywhere one likes. One may set it to be zero at the surface of the Earth, or may find it more convenient to set zero at infinity (as in the expressions given earlier in this section).A thing to note about conservative forces is that the work done going from A to B does not depend on the route taken. If it did then it would be pointless to define a potential at each point in space.
The electric potential produced by a point charge Q at a point a
distance r away is kQ/r.
For a collection of point charges Q1, Q2, Q3, , the electrostatic
potential energy is equal to U = (1/2)*Sum (i, j) k*Qi*Qj / r_ij, where r_ij is the distance between charges Qi
and Qj. The factor of 1/2 is inserted in order to avoid double counting. In other words, we sum over the pairs of
The electric field vector may be obtained from the electric
potential: E = -grad V; i.e., E is the negative of the gradient of V.
Electric Potential, Part 2
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