1. Chapter 21
Electric Fields

2. 21.1 Creating and Measuring Electric Fields
The Electric Field
The electric field is a vector quantity that relates the force exerted on a test charge to the size of the test charge.
Electric field E = F on q’ q’
The direction of the field is the direction of the force on the positive test charge.
A picture of an electric field can be made by using arrows to represent the field at various locations.

3. Picturing the Electric Field
Notice the field lines always leave a positive charge and enter a negative charge. Lines do not really exist. They are simply a means of providing a model of an electric field. Electric fields do exist!

4. 21.2 Applications of Electric Fields
Energy and Electric Potential
The electric potential difference, ΔV, is defined as the work done moving a test charge in an electric field divided by the magnitude of the test charge (q’)
Electric Potential Difference
ΔV = W on q’ q’

5. The Electric Potential in a Uniform Field
The electric potential difference, ΔV, between two points a distance d apart in a uniform field E, is represented by:
ΔV = Ed
The produce of the units E and d is (N/C)∙(m). This is equivalent to one J/C, the definition of one volt.

6. Millikan’s Oil-Drop Experiment
Robert A. Millikan in 1909 used the uniform electric field to determine the charge on a single electron.
He found experimentally that the changes in the charges of the oil drops were always multiples of 1.60 X C.

7. Sharing of Charge
All systems come to equilibrium when the energy of the system is at a minimum. Charges do the same thing when moving between charged conductors. They distribute themselves so that the net force on each charge is zero.
Earth is a very large conductor and can absorb all excess charge on a body. Touching a body to Earth to eliminate excess charge is called grounding.

8. Electric Fields near Conductors
Charges on a conductor spread as far as possible to make the energy of the system as low as possible. The result is that all charges are on the surface of a conductor. The shape of the conductor is also important and charges will be closer together at sharp points. A lightning rod is an example of this.

9. Capacitance C = q/ ΔV Storing Charges: The Capacitor
As charge is added to an object, the electric potential difference between the object and Earth increases. The ratio of the charge stored to the potential difference is called the capacitance, C. Capacitance is measured in farads, F. One farad is one coulomb per volt.
Capacitance C = q/ ΔV
The capacitance depends only on the construction of the capacitor, not on the charge, q.

10. PSS Sketch the problem. Draw the vector diagram.
List the known and unknowns.
Use the equations to relate the variables.
Check that the units are correct.
Solve the problem.
Check your answer.