Question

A. Consider a charge Q fixed in place at the origin that creates an electric field in the surrounding region. We call a charge which gives rise to the electric field the source charge. You bring a small charge q from infinite distance to a distance r from the source charge adiabatically, that is, infinitely slowly such that the electric field due to the source charge is not disturbed. This small charge q is called a test charge. Now answer the following questions. All of your answers will be in terms of q, Q, r and the dielectric constant εo, as appropriate and be careful about your signs. 1. What is the electric potential energy of the charge q as a function of the distance r away from

Answer 1

U = k Q q / r

Step-by-step explanation:

The potential electric energy for a point charge is

U = k q₁ q₂ / r

Where k is the Coulomb constant, q are the electric charges and r is the distance between them

Let's replace our values

U = k Q q / r

Note that the positive power is because the two charges have the same sign, so we have to do a job to move the test load and also a scalar