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.     F_E = kQq/r² → F_E 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)     E_byQ = kQ/r² = F_E/q → r represents distance to the other charge, or just a point in the field

(1)   Units are N/C or V/m

7.     Electric force and field:

a)     F_{on 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)     W_{by electric field} = -ΔPE_elec

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: F_elec = 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:
  • F_{on 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:
  • W_{by electric field} = -ΔPE_elec
• Change in KE:
  • KE = -ΔPE_elec

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