Equipotential Surfaces — Question 1

Question 1

Unequal spacing between equally spaced voltage levels reveals a stronger field

Locally parallel equipotentials have values 30, 20 and 10 V at x=0, .020 and .025 m respectively. Treat the field as uniform within each gap.

1. Find the field in each gap, including direction.

2. Find the work moving a $-3.00$ nC probe from the 30 V surface to the 10 V surface.

Question 1 - Solution

Unequal spacing between equally spaced voltage levels reveals a stronger field

(a) Method and calculation

$$E_{x,1}=-\frac{20-30}{.020}=+500\,\mathrm{V/m}.$$$$E_{x,2}=-\frac{10-20}{.005}=+2000\,\mathrm{V/m}.$$

(b) Interpretation and further calculation

$$\Delta U=q(10-30)=+60.0\,\mathrm{nJ}.$$$$W_e=-\Delta U=-60.0\,\mathrm{nJ},\qquad E_2/E_1=4.$$

Physical check

Smaller normal spacing for the same voltage interval implies a larger field; the negative charge is forced toward higher potential.