Question

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.

Short answer

Yes, it is appropriate to ask how much energy is gained by an electron but no it is not appropriate to ask what potential difference the electron moves through during a complete trip.

Step-by-step solution

Important Concept

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$\mathbf{=}\mathbf{∆}\mathbf{E}$

Application

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.