Equipotential Surfaces — Question 2

Question 2

An oblique path length must be projected onto the surface normal

Two parallel equipotential planes differ by 60.0 V. A straight path between them has length .200 m and makes $60.0^\circ$ with the normal. The field is uniform.

1. Find the normal separation and field magnitude.

2. Calculate the field work on a positive charge q traveling along the path from higher to lower potential and verify it using the force projection.

Question 2 - Solution

An oblique path length must be projected onto the surface normal

(a) Method and calculation

$$d=\ell\cos60^\circ=(.200)(.500)=.100\,\mathrm m.$$$$E=|\Delta V|/d=600\,\mathrm{V/m}.$$

(b) Interpretation and further calculation

$$W_e=qE\ell\cos60^\circ=q(60.0\,\mathrm V).$$$$W_e=q(V_{\mathrm{high}}-V_{\mathrm{low}})=q(60.0\,\mathrm V).$$

Physical check

Using the oblique length directly in E=|difference in V|/distance would underestimate the field.