Induced Electric Fields — Question 10

Question 10

A reversible flux pulse can return a track-bound particle to its initial speed

A charged particle on a frictionless circular track initially has angular momentum L0. An axisymmetric source changes the enclosed flux by DeltaPhi and later returns it exactly to the initial value. There is no radiation or dissipative force. Use $\Delta L_z=-q\Delta\Phi/(2\pi)$.

1. Find the intermediate and final angular momenta.

2. Find the net electric work over the complete pulse and explain how nonzero work can occur during each stage.

Question 10 - Solution

A reversible flux pulse can return a track-bound particle to its initial speed

(a) Method and calculation

$$L_{\mathrm{mid}}=L_0-q\Delta\Phi/(2\pi).$$$$\boxed{L_f=L_{\mathrm{mid}}+q\Delta\Phi/(2\pi)=L_0}.$$

(b) Interpretation and further calculation

$$W_1=\frac{L_{\mathrm{mid}}^2-L_0^2}{2mr^2},\quad W_2=\frac{L_0^2-L_{\mathrm{mid}}^2}{2mr^2}.$$$$\boxed{W_{\mathrm{total}}=0}.$$

Physical check

Zero final energy change here follows from the lossless constrained-particle model; it differs from the positive heat of a resistive pickup.