I. 7.1: ELECTRICAL CHARGE
A. Atoms (the protons and electrons) are held together because of the attractive force of their electrical charge
B. Positive/negative:
1. Electron charge = -e
2. Proton charge = +e
C. Elementary charge: e = 1.6*10-19 C
1. In virtually all cases, objects become charged by gaining or losing electrons
D. Quantized charge:
Charge can only be in whole numbers of +/- e’s
1. q = n(±e), where n is a positive integer
2. Total electric charge is always conserved → if you pet a cat, you rub electrons off the cat’s fur; your charge is more negative and the cat’s is equally more positive
II. 7.2: ELECTRICAL FORCE AND COULOMB’S LAW
A. Coulomb’s law:
1. FE = kQq/r2 → FE is electrical force between two charges
a) + means repulsive, – means attractive
b) k is proportionality constant and varies depending on material between particles
c) k0 = 9*109 N∙m2/C2 and assumes empty space between particles
(1) This is a huge number
B. THE PRINCIPLE OF SUPERPOSITION FOR ELECTRIC FORCES:
Describes how 2 or more charges affect a third
1. Total force is the vector sum of the forces
2. Principle of superposition: the net electric force on a charge (q) due to a collection of other charges (Q’s) is equal to the sum of the individual forces that each of the Q’s alone exert on q
III. 7.3: ELECTRICAL FIELDS
A. Electric field:
The area in which the existence of a charge alters the space around it
1. If a second charge happens to be there, it will feel the effect of the field created by the original charge
2. The electric force on a second charge q is exerted by the field rather than by the orginal charge
3. Source charge(s): the charge(s) that create the electric field
4. Vector field: describes an electric field, where each point in space around field is associated with a specific vector (tells strength and direction a positive test charge would feel)
5. Remember, two charges create a force, but one charge creates a field!
6. Electric field:
a) EbyQ = kQ/r2 = FE/q → r represents distance to the other charge, or just a point in the field
7. Electric force and field:
a) Fon q = qE → remember, F = kqQ/r2, so subsitute E for kQ/r2
B. THE PRINCIPLE OF SUPERPOSITION FOR ELECTRICAL FIELDS:
Describes how more than one souce charge combine to create a new electrical field
1. Electric dipole – a pair of equal but opposite charges
2. The force of a particle is always tangential to the field lin passing through that point
C. CONDUCTORS, INSULATORS, AND POLARIZATION
1. Conductor – materials that contain charges that are free to roam throughout the material
a) EX: A + charge nearby will pull electrons to one side of a metal ball, polarizing the ball
2. Dielectric (insulator) – material that does not have free charges; the electrons are tightly bound to the atom and cannot roam
a) EX: A + charge nearby will polarize each atom, which causes smaller electrical attraction
IV. 7.4: ELECTRICAL POTENTIAL
A. ELECTRIC POTENTIAL
(note → not to be confused with ELECTRIC POTENTIAL ENERGY):
1. Electrical field and electrical potential are similar, but potential is a scalar quantity (no direction)
2. Think of electric field just in terms of value (number)
3. Electric potential = voltage:
a) φ = kQ/r (Unit is VOLT (J/C))
4. Electic potential energy of a charge = voltage * charge
5. Change in electrical potential energy:
a) ΔPE = qΔφ = kqQ/r = qV (J)
6. Work done by electric field:
a) Wby electric field = -ΔPEelec
7. Kinetic energy as related to potential energy
a) ΔKE = -ΔPE → there is no friction to account for
B. THE PRINCIPLE OF SUPERPOSITION FOR ELECTRICAL POTENTIAL
1. This is easier than for electric fields because potential is scalar → just add potentials together
CHAPTER 7 SUMMARY
- Elementary charge: e = 1.6*10-19 C
- Charge of proton = +e; charge of electron = -e
- Charge is quantized: e = 1.6*10-19 C
- Coulomb’s law: Felec = kQq/r2
- Coulomb’s constant: k0 = 9*10-9 N∙m2/C2
- Principle of superposition:
- The net force, electrical field, or electric potential on a charge q (for force) or point P (for electric field or electric potential) due to a collection of other charges (Qs) is equal to the sum of individual effects of each Q.
- Electric field due to point charge Q:
- E = kQ/r2
- Duration of electric field:
- Positive charges want to move in the direction of the electric field (E)
- Negative charges want to move in the opposite direction of the electric field (E)
- Electric force and field:
- Fon q = qE
- Electric potential:
- φ = kQ/r
- Positive charges want to move to regions of lower potential (more negative)
- Negative charges want to move to regions of higher potential (more positive)
- Change in electrical PE:
- ΔPE = qΔφ = qV (J)
- Work done by electric field:
- Wby electric field = -ΔPEelec
- Change in KE:
- KE = -ΔPEelec
