Chapter 15 & 16

Electrostatics: Forces & Energy

Electric Potential

 

Potential of a Point-Charge

The Electric Potential for a Point Charge:

 

Electric Potential Energy for Point Charges q and Separated by a Distance r:

 

Example 16-5

Find the electric potential produced by a point charge of at a distance of 2.60 m.

 

Solution:

 

Example 16-6

A charge is placed at the origin, and a second charge equal to -2q is placed on the x-axis at the location x = 1.00 m. (a) Find the electric potential midway between the two charges. (b) The electric potential vanishes at some point between the charges; that is, for a value of x between 0 and 1.00 m. Find this value of x.

 

Solution:

(a)

(b)

 

Example 16-7

Two point charges, each equal to +q, are placed on the x-axis at x = -1 m and x = 1 m. As one moves along the x-axis, does the potential look like a peak or a valley near the origin?

 

 

Solution:

Near the origin, the potential looks like a valley.

 

Example 16-8

Two charges, +q and +2q, are held in place on the x-axis at the locations x = -d and x = +d, respectively. A third charge, +3q, is released from rest on the y-axis at y = d. (a) Find the electric potential due to the first two charges at the initial location of the third charge. (b) Find the initial electric potential energy of the third charge. (c) What is the kinetic energy of the third charge when it has moved infinitely far away from the other two charges?

 

Solution:

(a)

(b)

(c)

 

Equipotentials

Around a point charge there is a sphere that represents the same potential. If you put all of the spheres together in one figure you have an equipotential surface.

Field Lines and equipotentials for a small positive charge.

The equipotential surfaces are concentric spheres centered on the charge.

A continuous color representation of the potential.

The height of the peak corresponds to the size of the potential above the zero base level.

 

On to more Equipotentials