Evans SPH 4U1

Unit 6: Electricity

Note 5: Electric Potential

Reference: Chapter 7.4

Electric Potential Energy, Ee:

Recall: The magnitude of the force of gravity between any 2 masses is and

the gravitational potential energy between any 2 masses is    (if the zero value of Eg is chosen as when the 2 masses are infinitely apart)

Similarly, electric potential energy stored in the system of 2 charges, q1 and q2 is .

~ If q1 and q2 are opposite charges, they attract, and Ee is negative (as in the gravitational case when the masses attract).

~ If q1 and q2 are similar charges, they repel, and Ee is positive (i.e. energy is stored by moving them closer together).

~ The zero level of electrical potential energy is approached as the separation of the charges approaches infinity.

~ Scalar quantity measured in joules

Electric Potential, V:

~  the electric potential energy per unit positive charge (not to be confused with Electrical Potential Energy, Ee)

~ Scalar quantity

~ One volt is the electric potential when one joule of work is done in moving a charge of 1 coulomb from infinity to that point.

~ The electric potential of a charge at a point is the work done in bringing a positive charge from infinity to the point.

~ The electric potential at a point due to several point charges is the sum of the electric potentials at that point due to each charge.

Units are Volts (joules/coulomb)

Example:

Two charges 5.4 x10-7C and 3.6 x 10-7C are 36 cm apart. What is the electric potential midway between these charges? (4.5 x 104 J/C)

Change in Electric Potential Energy (Work):

In moving a charge from point A to point B the work done will be equal to the change in electric potential energy

Change in Electric Potential Energy Between 2 Parallel Plates:

Often we will be interested in the potential difference between 2 points in a uniform electric field (between parallel plates).

Note: From the + plate to the - plate we have a decreasing potential. From the - plate to the + plate we have an increasing potential.

Recall:     and therefore

**

**Note that we can only use this in cases where the Electric Field is constant over a distance such as in our case of parallel plates where it is a uniform electric field.. We can not use it for point charges where the charge is being moved through a distance where the Electric Field can vary.

(this is similar to using mgh near the earth's surface but not at farther distances)

Now using substitution:

Example:

In the diagram (see blackboard), sphere A has a charge of 3.0 x 10-5C and sphere B has a charge of -2x10-5 C. They are placed 160cm apart.  Point P is 20 cm from A and point M is midway between the two charges.

Find:

a) the electric potential difference between M and P. (-1.1 x 106 volts)

b) the work done in moving a charge of 2.0 x 10-8 C from P to M. (-2.2 x 10-2 J)

Text Questions:

Page 354 #'s1-4 (warm up questions)

Page 358 Practice Question #6

Page 358-359 #'s 7-9