A charge q=50 μC is moved slowly from node n to node p

A charge \(q=50\,\mu\mathrm{C}\) is moved slowly from node n to node p. The electrostatic potential at n is \(v_n=8\,\mathrm{V}\) and the potential at p is \(v_p=-12\,\mathrm{V}\), both measured with respect to a common reference node 0. Define \(v_{pn}\) with the plus reference at p and the minus reference at n. Determine \(v_{pn}\), \(v_{np}\), and \(v_{n0}\). Compute the change in electric potential energy of the charge as it is taken from n to p, and compute the work done by the electrostatic field on the charge during that move. State whether the charge gained or lost potential energy.

\(v_{ab}\) is the potential of node a minus the potential of node b; energy of a charge at a node is \(qv\) relative to the reference.