CH 22: Electric Fields and Gauss’s Law

Every charge generates an Electric Field. Electric Field – Region of influence surrounding any charged object. Interaction between electric fields results in a force between the sources of the electric fields. Electric Field Lines are used to show direction of the electric field. (electric field lines are used as a means of visualizing the electric field, but there are not really lines emanating from the charge) Positive charges are defined to have electric field lines directed away from the charge (source). Negative charges are defined to have electric field lines directed towards the charge (sink). Electric field lines for a positive charge Electric Field Lines: Can never cross Have a direction denoted by an arrow The number of field lines drawn is proportional to the amount of charge and hence the strength of the electric field generated. Electric field lines for a negative charge

Dipole – two opposite charges Courtesy of NASA Point Charge 3D Dipole Courtesy of NASA Dipole – two opposite charges Courtesy of UVI Repulsion Attraction

6. some other combination 7. None of the above. Consider the four field patterns shown. Assuming there are no charges in the regions shown, which of the patterns represent(s) a possible electrostatic field: 1. (a) 2. (b) 3. (b) and (d) 4. (a) and (c) 5. (b) and (c) 6. some other combination 7. None of the above. Answer: 2. Pattern (a) can be eliminated because field lines cannot simultaneously emanate from and converge at a single point; (c) can be eliminated because there are no charges in the region, and so there are no sources of field lines; (d) can be eliminated because electrostatic field lines do not close on themselves.

Determination of the magnitude and direction of an electric field The magnitude of the electric force is directly related to the strength of the electric field. The direction of the electric force is in the same direction as the electric field when acting on a positive charge. The direction of the force is opposite for a negative charge! Fe = electric force applied to charge q q = charge within an electric field E = electric field strength Fe = qE Electric fields are vectors and must be dealt with appropriately!!

The electric field strength decreases with distance from the charge creating the electric field in a manner similar to the electric force. } Electric field due to a point charge Vector forms of electric field

Example: A positive 30 mC point charge is in an isolated region of space. What is the electric field strength at a point P 5 cm from this charge? If a negative 20 mC charge suddenly appears at a distance of 10 cm from the original charge, what is the electric field strength at point P halfway between the two charges? If a small 1 mC positive test charge is placed at point P, what is the net force on this test charge? a) 30 mC E1 P 5 cm Left

b) 30 mC 20 mC E E1 P E2 5 cm 5 cm Left Left

c) 30 mC 20 mC 1 mC E P F 5 cm 5 cm Left

Continuous Charge Distribution Not all charged object have negligible dimensions. The electric field contributions from different parts of the charged object varies with the distance that small part is from the point of interest. Each section does not have to have the same amount of charge. The contribution from each part must be summed to get the net electric field strength Dq is a small segment of charge DE is a small contribution to E dq is an infinitesimal segment of charge dE is an infinitesimal contribution to E

Charge Density We can substitute our small segment of charge dq with a charge distribution relationship. This charge distribution relationship is used to simplify our calculations of the electric field of a continuous object. The charge distribution relationships are usually related to the geometry of the charged object and hence called charge density. Types of charge densities: Q is the total charge contained within the object Volume charge density (r) Surface charge density (s) Linear charge density (l) dq = rdV dq = sdA dq = ldl