# PHYS 142 Lecture Notes - Lecture 10: Equipotential, Electric Field

PHYS 142: Electromagnetism and Optics - Lecture 10: Potential and Field Part 2

Finding the Electric Field from the Potential:

● The figure shows two points i and f separated by

a small distance Δs.

● The work done by the electric field as a small

charge q moves from i to f is W = FsΔs = qEsΔs.

● The potential difference between the points is:

● The electric field in the s-direction is

Es = − ΔV/Δs. In the limit Δs → 0:

● Suppose we knew the potential of a point charge to be V = q/4π

∈0

r but didn’t remember

the electric field.

● Symmetry requires that the field point straight outward from the charge, with only a radial

component Er.

● If we choose the s-axis to be in the radial direction, parallel to E, we find:

● This is, indeed, the well-known electric field of a point charge

● Graphically, the electric field is the negative of the slope of the graph of the potential.

Kirchhoff’s Loop Law:

● For any path that starts and ends at the same point:

● The sum of all the potential differences encountered while moving around a loop or closed

path is zero.

● This statement is known as Kirchhoff’s loop law.

Conductors in Electrostatic Equilibrium:

● Properties of such conductors:

▪ All excess charge sits on the surface.

▪ The surface is an equipotential.

▪ The electric field inside is zero.

## Document Summary

Phys 142: electromagnetism and optics - lecture 10: potential and field part 2. The figure shows two points i and f separated by a small distance s. The work done by the electric field as a small charge q moves from i to f is w = fs s = qes s. The potential difference between the points is: The electric field in the s-direction is. Suppose we knew the potential of a point charge to be v = q/4 0 r but didn"t remember. Symmetry requires that the field point straight outward from the charge, with only a radial the electric field. component er. If we choose the s-axis to be in the radial direction, parallel to e, we find: This is, indeed, the well-known electric field of a point charge. Graphically, the electric field is the negative of the slope of the graph of the potential. For any path that starts and ends at the same point: