Question

derive an expression for electric potential due to point charge

Answer 1

Point charges, such as electrons, are among the fundamental building blocks of matter. Furthermore, spherical charge distributions (like on a metal sphere) create external electric fields exactly like a point charge. The electric potential due to a point charge is, thus, a case we need to consider. Using calculus to find the work needed to move a test charge  from a large distance away to a distance of from a point charge , and noting the connection between work and potential , it can be shown that the electric potential  of a point charge is



where k is a constant equal to
.

Electric Potential  of a Point Charge

The electric potential  of a point charge is given by



The potential at infinity is chosen to be zero. Thus  for a point charge decreases with distance, whereas  for a point charge decreases with distance squared:



Recall that the electric potential  is a scalar and has no direction, whereas the electric field  is a vector.