Two Experiments — Question 8

Question 8

A slotted pickup interrupts conduction without removing the changing flux

Two otherwise identical pickup loops surround the same changing source. Loop A is closed with resistance R; loop B has a narrow insulating gap. An ideal high-impedance detector spans the gap with leads routed together. The supplied loop emf magnitude is E.

1. Compare the steady quasistatic conduction currents and resistive heating.

2. For finite detector resistance Rm much greater than R, estimate the gap voltage and the loading error.

Question 8 - Solution

A slotted pickup interrupts conduction without removing the changing flux

(a) Method and calculation

$$|i_A|=E/R,\quad P_A=E^2/R.$$$$R_m\to\infty:\quad\boxed{i_B\to0,\ P_B\to0}.$$

(b) Interpretation and further calculation

$$i_B=\frac E{R+R_m},\quad |V_m|=\frac{ER_m}{R+R_m}.$$$$\boxed{\frac{E-|V_m|}{E}=\frac R{R+R_m}\simeq R/R_m}.$$

Physical check

The gap does not eliminate the induced emf. The stated voltage assumes tightly paired measurement leads and the prescribed flux-linking contour.