FACULTY OF SCIENCE, WINTER 2008
PHYS 126 LEC B3 : Fluids, Fields and Radiation
(Instructor: Marc de Montigny)
Walker, Physics, Chapter 20: Electric Potential and Electric Potential Energy
- Section 20-1: Electric Potential Energy and the Electric Potential
- P. 663, Eq. 20-1, Electric potential energy: ΔU = -W = qEd.
- P. 663, Eq. 20-2, Electric potential: ΔV = ΔU/q = -W/q = -Ed
- Unit: 1 Volt (V) = 1 J/C
- Remarks:
- Like potential energy, electric potential is a scalar quantity.
- Analogy with gravitational force ΔUgrav = mgh. Gravitational
potential would be ΔVgrav = ΔUgrav/m = gh.
- Potential (electric or gravitational) decreases in the direction of the field.
See P. 665, Figure 20-3.
- P. 663, Figure 20-1 shows the analogy between
gravitational and electric potentials.
- P. 664, Eq. 20-4, Connection between the electric field and the electric potential:
E = -ΔV/Δs (where Δs is the distance between two points).
This is illustrated in P. 664, Figure 20-2.
- From Eq. 20-4, we see that Units of E are Volts/meter = V/m
- The gravitational analogy of Eq. 20-4 is
-ΔVgrav/h = -gh/h = -g, where the sign shows that the
field points downward.
- Unit of energy: 1 electron-volt (eV) = 1.60×10-19 J
- P. 689, Problem 10
- P. 690, Problem 14
- Section 20-2: Energy Conservation
- ΔK + ΔUel = 0. Also expressed in terms
of electric potential as: ΔK + q ΔVel = 0.
- Explicitly, ½mvA2 + q VA
= ½mvB2 + q VB
- Positive charges accelerates in the direction of decreasing
potential; negative charges, in the opposite direction.
- P. 690, Problem 18
- P. 690, Problem 19
- Section 20-3: The Electric Potential of Point Charges
- Similar to the Gravitational Forces, discussed in Chap 12.
There we have seen that Ugrav = -Gm1m2/r,
Eq. 12-9.
- P. 669, Eq. 20-8, Uel = kq1q2/r.
- Question: Why don't we have a sign, as in the gravitational relation?
- (For those who are familiar with calculus, a force F is derived from potential
energy as F = - U'.)
- P. 669, Eq. 20-7, Vel = kq/r.
- P. 670, Superposition of the Electric Potential: The total electric potential
due to two or more charges is equal to the algebraic sum of the potentials due
to each charge separately. (Algebraic means that V can be positive or negative.)
- P. 690, Problem 24
- P. 690-692, Problems 23 and 65
- P. 691, Problem 32
- Section 20-4: Equipotential Surfaces and the Electric Field
- Equipotentials surfaces refer to a set of adjoining points for which the
electric potential is the same.
- A two-dimensional gravitational analogue is the
contour map. To each point of the earth's surface corresponds a level
(anal. potential); the locus of points with fixed level defines an equipotential
surface (actually, here, a curve).
- P. 674: The electric field is always perpendicular to the
equipotential surface, and it points in the direction of decreasing
electric potential.
- External Website on
Electric Potential,
External Website
on Equipotential Surfaces
- P. 691, Problem 39
- P. 675: Ideal conductors are equipotential surfaces, that is,
every point on or within an ideal conductor is at the same potential.
(The reason is that E = 0 inside the conductor.) Thus the electric
field is perpendicular to the surface of a conductor.
- P. 676, Figure 20-10 shows why charge density is
greater near sharp ends. Explanation at bottom of P. 675 and top of P. 676.
- Section 20-5: Capacitors and Dielectrics
- A capacitor is a device that stores electric charge.
In its simplest form, it consists of two conductors, called plates, one with charge
+Q, the other with charge -Q.
- P. 678, Eq. 20-9, Capacitance: C = Q/V
- SI Unit: 1 farad (F) = 1 C/V
- C = 1 F would be enormous. Typically C is of the order of nanofarads (1 nF = 10-9 F),
picofarads (1 pF = 10-12 F) or femtofarads (1 fF = 10-15 F).
- The capacitance, C, of a capacitor is defined as the amount of charge
Q stored in this capacitor per volt of potential difference V between the
two plates of the capacitor.
- For a parallel-plate capacitor,
we have, from P. 679, Eq. 20-12, C = ε0 A/d, where
A is the area of each plate and d the distance between the two plates.
- ε0 = 8.85×10-12
C2/N•m2
- P. 692, Problem 47 (a)
- P. 692, Problem 62
- A dielectric is an insulating material that increases the capacitance
of a capacitor, by reducing the field between the two plates, as
shown in P. 681, Figure 20-15.
- P. 681, Eq. 20-14, C = κ C0 (C0
denotes the capacitance with vaccuum between the plates).
Correspondingly the fields, with and without dielectric, are related
by E = E0/κ, with κ, the dielectric constant.
P. 681, Table 20-1 gives the dielectric
constants of some substances.
- P. 692, Problem 47 (b)
- P. 683, defn: the dielectric strength of a dielectric material
is the maximum electric field this material can withstand before
breakdown. Dielectric breakdown occurs when the electric field is
large enough to tear the constituting atoms apart, thereby allowing
the dielectric to conduct electricity. Some value of dielectric strength
are given in P. 683, Table 20-2. An
example is a spark (or a bolt of lightning) in air.
- P. 692, Problem 49
- Section 20-6: Electrical Energy Storage
- Electrical energy stored in a capacitor:
- P. 683, Eq. 20-16: U = ½QV
- P. 683, Eq. 20-17: U = ½CV2
- P. 684, Eq. 20-18: U = Q2/2C
- P. 685, Eq. 20-19, Energy density:
uE = ½ ε0E2
- P. 692, Problem 59
Back to
PHYS 126, LEC B3 Webpage
