In the situation shown in Fig. 29.18, would it be appropriate to ask how much energy an electron gains during a complete trip around the wire loop with current I′? Would it be appropriate to ask what potential difference the electron moves through during such a complete trip? Explain your answers.

The net work done by forces on a body equals the change in its kinetic energy $\left(∆E\right)$, according to the work-energy theorem.

Work Done$\mathbf{=}\mathbf{∆}\mathbf{E}$

Yes, it is appropriate to ask how many energy an electron gains during a complete trip. When an emf is induced in the loop, there is an induced electric field of non-electrostatic origin. This field is non-conservative.

Thus, there is a work done on the electron after it moves a complete round, this work is given by:

$$\begin{gathered} \mathrm{Work}={\mathrm{E}}_{\mathrm{gained}} \\ =\mathrm{e\epsilon } \end{gathered}$$

Here, ${\mathrm{E}}_{\mathrm{gained}}$is the gained kinetic energy, is the charge, and $\mathrm{\epsilon }$is the emf.

No, it is not appropriate to ask what potential difference the electron moves through during a complete trip. Since the field is non-conservative and can not be associated with potential, the loop is equipotential and the potential difference between any two points on the loop is zero.