Induced Magnetic Fields — Question 5

Question 5

Two radial magnetic measurements locate the changing electric-field boundary

A uniform axial electric-field rate fills an unknown radius a. At r1=.0200 m inside, B1=$2.00\times10^{-8}$ T; at r2=.100 m outside, B2=$1.80\times10^{-8}$ T. Directions agree. Use the quasistatic circular formulas and $c=3.00\times10^8$ m/s.

1. Infer a and the electric-field rate.

2. Check that the assumed inside and outside locations are self-consistent.

Question 5 - Solution

Two radial magnetic measurements locate the changing electric-field boundary

(a) Method and calculation

$$B_1=\dot E r_1/(2c^2),\quad B_2=\dot E a^2/(2c^2r_2).$$$$\boxed{a=\sqrt{(B_2/B_1)r_1r_2}=.0424264\,m}.$$

(b) Interpretation and further calculation

$$\dot E=2c^2B_1/r_1=1.80\times10^{11}\,V/(m\,s).$$$$\boxed{r_1=.0200<a=.0424264<r_2=.100}.$$

Physical check

The outside field records total changing flux while the inside field records the local uniform rate.