No Slide Title

Potential

1Problems with electric field strength equations:Good: Allows the use of Newtons 2nd Law.Bad: 1. E is a vector. 2. Due to the number of possible charges it could be quite complicated. 3. Works best with static situations.

2

When a charge is moves in an electric field a force is acting on that charge.Combination of force and displacement means work is being done:

From conservation of energy:

Combine this with the definition of E:

3Problems with electric work equations:Good: Not a vector. Allows the use of Conservation of Energy.Bad: Still difficult for lots of particles. Still difficult for moving particles.

4Ultimate Solution: Set up a ratioVoltage: Ratio of Energy per unit charge.

U = Energy (joules)q = Charge (coulombs)V = Voltage (volts)

5Warning!Potential or Electric Potential or Potential Drop - Work/Energy.Voltage or Voltage Drop - Energy PER charge.Unfortunately many physicists, engineers, technicians etc use all five to mean voltage.

6Voltage measures energy per charge i.e. in a situation where V = 12 V, 1 C of charge can do 12 J of work, 2 C, 24 J etc.Can now use conservation of energy to solve problems.If you know the voltage you no longer worry about the charge distribution!

7Advantages: Scalar +/- but no directions Typically know energy available since we supply that (battery). Can deal with moving charges without major calculations every time something is movedProblem: Still need to develop specific equations for each type of charge distribution BUT there are only a handful of standard situations in a circuit AND once formula is developed no need to do again.

8Example: Point Charge

Note: The path from A to B is parallel to the force lines so cos = 1

9So what, or where, is zero voltage? For fields in free space zero is at infinity For circuits zero can be: Negative terminal of the batteryGroundAny arbitrary point in the circuit

10

11

12Generic EquationsVoltage:

13If you have an equation for E and want V you integrate.If you have an equation for V and want E you differentiate.However E is a three dimensional function so you can NOT take a standard derivative.You must use partial derivatives.

14Everything you really need to know about partial differentials.(at least for this class)

If the x, y and z components of the function are independent of each other simply take the derivative of the function with respect to one component while treating the others as constants.

15Example 1: At one time it was assumed that the energy needed to raise water from the surface of the Earth up to cloud level was provided by lightning. A typical lightning flash transfers 4 C of charge and 4.2 MJ of energy to the Earth. (a) What is the potential difference between the cloud and the ground? (b) A low level cloud is any cloud with a base below 2000 m altitude. What weight of water could be lifted to an altitude of 1000 m by the energy?

(a)

Example 1: At one time it was assumed that the energy needed to raise water from the surface of the Earth up to cloud level was provided by lightning. A typical lightning flash transfers 4 C of charge and 4.2 MJ of energy to the Earth. (a) What is the potential difference between the cloud and the ground? (b) A low level cloud is any cloud with a base below 2000 m altitude. What weight of water could be lifted to an altitude of 1000 m by the energy?(b)

Just for funUSA Today quotes Peggy LeMone, senior scientist at the National Center for Atmospheric Research, as saying that a thunderstorm cloud contains approximately 275 million gallons of water. (http://www.usatoday.com/weather/resources/askjack/archives-thunderstorms.htm}Converting our 107 kg into gallons using the density of fresh water gives then calculating the number of lightning strikes required gives:

Claims of 5000-8000 lightning strokes per hour have been made. Assuming 10,000 per hour would mean a storm would have to last 970 hours or 41 days. Not probable.

Example 2: Two large parallel conducting plates are 12 cm apart and have charges of equal magnitude and opposite sign on their facing surfaces. An electrostatic force of 3.9x10-15 N acts on an electron placed anywhere between the plates. What is the (a) electric field between the plates? (b) the potential difference between the plates?

Example 3: The electric potential is given by V = (2x2) - (3y4) + sin2z.What are the magnitude and direction of the electric field at (3,2,0)?

21