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

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Course 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 = − ΔVs. 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.
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## 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:

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