Physics 123 Concepts - Summary
Last updated December 3, 2010, 2:15 pm
Includes Chapters 19, 20, 21, 22, 23, 24, 25, 29, 30, 31, 32 (Fall 2010)
Note: Although I have done my best to check for typos and list the formulas correctly, you should verify the formulas are correct before using them. Make sure you know what all the variables represent in any particular formula. Some letters are used in different formulas from different chapters and may represent different things. - Dr. Nazareth
Chapter 19 (Electric charges, forces and fields) – updated for current textbook – 9/22/10
Electric charge (19.1)
· Intrinsic property of matter
· Two types: positive and negative
· Magnitude of charge on an electron or a proton = e
· SI units = coulomb (C)
· e = 1.60 x 10-19 C
· electric charge is quantized – it can only be an integer multiple of e
Electric conductors and insulators (19.2)
· insulator: material where charges are not free to move
· conductor: materials that allow charges to move somewhat freely
· semiconductor: material with properties in between conductors and insulators
Coulomb’s Law - Electrostatic Force (19.3)
· Law of conservation of electric charge
· “Like charges repel and unlike charges attract each other.”
· Electrostatic: all charges are at rest
· Coulomb’s Law
o (magnitude only)
· note absolute value of point charges used
· r = distance between the point charges
· SI units = Newton (N)
· direction – acts along line between the two point charges and is attractive for oppositely charged point charges and repulsive for like charged point charges
· k = 8.99 x 109 N·m2/C2
o Similar in form to Newton’s law of gravitation, except, force may attract or repel, depending on signs of the charges
o If more than two charges, than total force on a charge is the vector sum of the forces from each pair. Break problem into parts and calculate the net force (vector sum). See chapter 19, examples 19-2 and 19-3, pgs. 661-663
o If total charge of Q is distributed over surface of a sphere, then treat sphere as a “point” located at the center of the sphere.
· Q = σA (σ = surface charge density; A = surface area of sphere)
· A = 4πR2 (R = radius of sphere)
· (q is located outside sphere at distance r from center)
Electric Field (19.4-19.5, some 19.6)
· Definition
o E = F/q0
o SI units = Newton per coulomb (N/C)
o Vector quantity – direction same as direction of electric force on positive test charge
o Test charge, q0
· Small enough not to disturb surrounding charges
· Positive
· “the electric field is the force per unit charge at a given location” pg 665
o If you know E, then force felt by charge q is F = qE
o Direction of force depends on sign of charge q
· If q = + then F same direction as E
· If q = - then F opposite direction as E
· Point charge
o (magnitude only - direction depends on whether q is + or -)
· Points radial out for q = + and radial in for q = -
o If have more than one point charge, then the electric field, E, is just the vector sum of the electric fields due to each charge separately, at that particular location
· See example 19-5, pg 668-669
· Electric field lines = lines of force
o Point from + charges to – charges
o Do not stop or start midspace
· Start at positive charges or infinity
· End at negative charges or infinity
o Density is proportional to field strength (more lines per area when field is stronger)
· Parallel plate capacitor
o See figure 19.17
o (magnitude only; only between plates away from edges)
· σ = q/A = charge per unit area = charge density
· E points from positively charged plate to negatively charged plate
· Inside a conductor (19.6)
o At equilibrium (electrostatic conditions)
· any excess charge is on surface of conductor
· E = 0 at any point inside the material of the conductor (not a cavity within the conductor)
· E just outside conductor is perpendicular to surface
· Conductor shields inside from outside charges, but doesn’t shield outside world from charges enclosed within
· Sharp point in a conductor – charges more densely packed here so the electric field is more dense outside sharp point
Charging by Induction (19.6)
· Charge an object without making direct physical contact
· How to:
o connect object to ground using a grounding wire
o bring charged rod nearby – the like charge is repelled away down the grounding wire (now object has net charge)
o remove grounding wire while charged rod still in place
o now remove rod and excess charge distributes itself about the object
· NOTE: induced charge is opposite charge of that on charged rod (object charged by touch has the same charge as the charged rod)
Gauss’s Law (19.7)
· Electric flux: Φ=EA cosθ
o E = electric field magnitude
o A = area of surface
o θ = angle between direction of E and the perpendicular to the area A
o think of electric field lines “flowing” through the surface of area A
o SI unit: N m2/C
o if surface A is closed (like a sphere - a rectangle would be open)
· flux is positive if E field lines are leaving the enclosed surface
· flux is negative if E field lines are entering the enclosed surface
o Permittivity of free space, ε0 = 1/(4πk) = 8.85 x 10-12 C2/(N·m2)
· Gauss’s law: if charge q is enclosed by any arbitrary surface, Φ = q/ε0
o shape of surface doesn’t have to be a sphere!!!
· Use Gauss’s law to find the electric field in highly symmetric situations
Chapter 20 (Electric Potential and Electric Potential Energy) – updated for current textbook – 10/3/10
· NOTE: textbook uses U for electric potential energy and I use EPE
Electric Potential Energy and the Electric potential (20.1)
· As charge moves from A to B, work WAB is done by electric force:
o WAB = EPEA - EPEB
o EPE = electric potential energy
§ SI units = joule (J) = N·m
· For a positive test charge, q0, moving upward a distance, d, in a downward pointing uniform electric field
o W = -q0Ed
o Since ΔPE = -W, then ΔPE = q0Ed
o Electric force does negative work to move positive charge upward so the change in potential energy is positive (it gets larger)
o Compare this to lifting a ball upward in the gravitational field … the potential energy gets larger as you lift the ball higher
· For a negative test charge, q0, moving upward a distance, d, in a downward pointing uniform electric field, the change in potential energy is negative (gets smaller) because the electric force does positive work to raise the negative charge upward
· CHANGE IN ELECTRICAL POTENTIAL ENERGY DEPENDS ON SIGN OF CHARGE AND ITS MAGNITUDE
· Electric potential, or simply, potential
o
o SI units = volt (V) = joule/coulomb (J/C)
o Not a vector quantity, but can be positive or negative
o Electric potential and electric potential energy are NOT the same thing
· Cannot determine V or EPE in the absolute sense because can only measure the differences, ΔV and ΔEPE, in terms of the work, WAB
o just like the gravitational potential energy is always relative to a reference level (e.g., ground level = 0 gravitational potential energy)
· Potential difference
o
o “a positive charge accelerates from a region of higher electric potential toward a region of lower electric potential”
· Electron volt: energy change an electron has when it moves through a potential difference of 1 V.
o 1 eV = e(1V) = (1.60 x 10-19 C) (1 V) = 1.60 x 10-19 J
· Connecting electric field and rate of change of electric potential difference
o SI units = volts/meter = V/m
o “the electric field depends on the rate of change of the electric potential with position.” Pg. 693, Physics, 4th ed., J.S. Walker, 2010.
§ Can think of V like height of a hill and E as the slope of that hill
o Electric potential decreases as you move in same direction as the electric field
§ Can think like going downhill … potential decreases
o In general, only gives component of E along displacement, Δs
§ ΔV = -ExΔx (displacement in x-direction)
§ ΔV = -EyΔy (displacement in y-direction)
Energy Conservation (20.2)
· Total energy now Etotal = KEtranslational + KErotational + PEgravitational + PEspring + PEelectrical
o Etotal = ½ mv2 + ½ Iω2 + mgh + ½ kx2 + EPE
· EPE = qV
· If no work is done by non-conservative forces, then energy is conserved
o Initial Energy = Final Energy = E0 = Ef
o Electrostatic (electric) force is conservative
· “Positive charges accelerate in the direction of decreasing electric potential.” pg 696, Walker
o (can think: positive charges speed up rolling “downhill”)
· “Negative charges accelerate in the direction of increasing electric potential.” pg 696, Walker
· For both positive and negative charges, as they accelerate, they move to a region of lower electric potential energy
Electric Potential Difference from point charges (20.3)
· SI units = volt, V
o V above not absolute, but rather how potential differs at a distance, r, as compared to a distance of infinity from the point charge.
o Assumes V = 0 at r = ∞
o So a positive q, puts potential everywhere above the zero reference value.
o So a negative q, puts potential everywhere below the zero reference value.
o Can add the potential from multiple point charges at a location
§ Its an algebraic sum (meaning signs matter), NOT a vector sum
§ See chapter 20, examples 20-3 and 20-4
· Electric potential energy for point charges q and q0 separated by distance, r
o EPE = q0V = kq0q/r SI units = Joule, J
· Note: r = distance NOT displacement so r is always positive
Equipotential surfaces (20.4)
· Potential is same everywhere on an equipotential surface
· “The net electric force does no work as a charge moves on an equipotential surface.”
· Electric field is
o always perpendicular to an equipotential surface
o points in direction of decreasing potential
· “Ideal conductors are equipotential surfaces; every point on or within such a conductor is at the same potential.” Pg. 703, Physics, 4th ed., J.S. Walker, 2010
o electric field lines meet the conductors surface at right angles
Capacitors (20.5)
· Stores electric charge, thus it stores energy
· Capacitance
o Q = CV
o SI units of capacitance = farad (F) = coulomb/volt (C/V)
o Depends on the geometry of the capacitor plate (or conductors) and the dielectric constant of material between the plates
o Parallel plate capacitor without a dielectric,
· A dielectric can be inserted between the plates of a capacitor to increase the capacitance
o Reduces electric field between plates in the dielectric. This increases the amount of charge that can be stored for a given electric potential difference between the two capacitor plates.
o Dielectric constant, κ = E0/E (unitless)
§ κ > 1
o Parallel plate capacitor with a dielectric,
o C = κC0 (applies to any capacitor, not just parallel plate)
· Dielectric breakdown: when the electric field applied is large enough to force the dielectric to conduct electricity
o Dielectric strength: maximum e-field before breakdown
§ See table 20-2, pg 711, Physics, 4th, J.S. Walker, 2010
Electrical Energy Storage (20.6)
· Energy stored – work done to charge up plates, increasing potential difference
o This work “stored as electric potential energy in the capacitor”
o
· Where is energy of a capacitor stored? In the electric field between the plates
o Energy density = uE=
o True for any electric field whether in capacitor or not
§ κ=1 if no dielectric uE = (½)ε0E2
Chapter 21 (Electric Current and DC Circuits) – updated for current textbook – 10/08/10
Electromotive “force” and current (21.1)
· Electromotive “force”, emf = maximum potential difference between the terminals of a generator or battery in a circuit
o NOT a real force … comes from historic description
· Electric current,
o SI units = ampere (A) = coulomb/second (C/s)
o Direct current (dc) – charge moves around circuit in same direction all the time
§ Batteries produce dc current
o Alternating current (ac) – charges move first one way then the other, then back, and so forth (Discussed in chapter 24)
· Emf controls work that battery must do to move charge around a circuit
o W = DQe
· Conventional current – hypothetical flow of positive charges in the circuit
o Flows from positive terminal of battery through circuit to negative terminal
o Flows from higher potential to lower potential (hence the positive → negative)
o In reality, negatively charged electrons flow in the circuit and go the opposite direction of the conventional current