Induced Electric Fields — Question 8

Question 8

Two electric-field measurements determine a hidden changing-flux radius

A uniform changing axial field is confined to unknown radius a. Clockwise induced electric-field magnitudes are .0300 V/m at r1=.0200 m inside and .0120 V/m at r2=.100 m outside. Assume axial symmetry with no added electrostatic field.

1. Infer the positive rate beta of axial field increase.

2. Infer a and verify that the assumed inside/outside classification is consistent.

Question 8 - Solution

Two electric-field measurements determine a hidden changing-flux radius

(a) Method and calculation

$$|E_1|=\beta r_1/2\Rightarrow\boxed{\beta=2(.0300)/.0200=3.00\,\mathrm{T/s}}.$$$$|E_2|=\beta a^2/(2r_2)\Rightarrow a^2=2r_2|E_2|/\beta.$$

(b) Interpretation and further calculation

$$a=\sqrt{2(.100)(.0120)/3.00}=\boxed{.0282843\,\mathrm m}.$$$$\boxed{.0200<a<.100}\quad\text{as assumed}.$$

Physical check

An exterior electric-field measurement measures the enclosed flux-change rate, while the interior measurement isolates the local field-change rate.