Question

What is the nature of symmetry of electric potential due to singke charge and why?

Answer 1

Answer:

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. To find the voltage due to a combination of point charges, you add the individual voltages as numbers. To find the total electric field, you must add the individual fields as vectors, taking magnitude and direction into account. This is consistent with the fact that  is closely associated with energy, a scalar, whereas  is closely associated with force, a vector.