AP Physics C
Review Guide: Chapters 23-24
Chapter 23: Electric Fields
Electric Charge:
Two types: + and Opposite attract
Ben Franklin
Likes repel
Charged can attract neutral
Charge is conserved
Charge is quantized: e = 1.6x10-19 C
Robert Millikan (Oil Drop Experiment)
Conductors / Insulators / Semiconductors: Know examples
Charging methods:
Friction (ebonite/fur and glass/silk) – End result: equal & opposite charge
Contact – End result: same type charge
Induction (grounding, induced charge separation) – End result: opposite charge
Force & Field are Vectors: Use diagrams and vectors for direction. Don’t use signs in equations
k=
k = 9 ×10 9 N ⋅ m2 /C 2
Point Charges:
€
In general:
kq1q2
r2
€
Fel = qE
Fel =
1
4 πεo
εo = 8.85 ×10−12 C 2 /N ⋅ m2
Coulomb’s Law
E=
kQ
r2
E=
Fel
q
€
€
Continuous Charge Distribution:
dq
E=k∫ 2
€
r
Know how to use
Examples:
Electric Field Lines:
€
kQ
E=
€ d( L + d)
λ=
Q
L
From end of
line charge
E=
€
€
€
σ=
kQx
( x 2 + R2 )
32
€
Show direction of force on positive test charge
Line density shows the strength of the E field
Emanate from positive and€terminate on negative charges
Never intersect
Negative charges move opposite field lines
Charges particles undergo uniform acceleration in a uniform electric field.
Think of field as force “waiting to happen”!
Q
€
A
ρ=
Q
V
Along axis of
ring charge
AP Physics C
Review Guide: Chapters 23-24
Chapter 24: Gauss’s Law
Electric Flux:
Gauss’s€Law:
€
r r
ΦE = Ε • Α = EAcos θ
r
r
ΦE = ∫ Ε • dΑ
Plane Area & Uniform Field
General
The net electric flux through a closed surface is proportional to the charge enclosed.
ΦE (closed) =
qin
εo
r
r qin
Ε
•
d
Α
=
∫
εo
Use this form to derive formulas for electric field.
(useful for cases with symmetry)
Gaussian
Surfaces
Electric€Fields Derived using Gauss’s Law
k=
k =€9 ×10 9 N ⋅ m2 /C 2
€
Non-conducting Uniform
Spherical Distribution:
E=
kQr
R3
1
4 πεo
εo = 8.85 ×10−12 C 2 /N ⋅ m2
r<R
E=
€
€
Thin Spherical Shell:
€
Infinite Line:
€
Any Conductor in
Electrostatic Equilibrium:
€
E =0
€
λ
E=
2πε r
€ o
E =0
r<R
kQ
r2
r≥R
kQ
E= 2
€ r
r≥R
€
σ
E=
Plane of Charge:
2εo
€
σ €
E=
Inside Conductor
Outside at Surface
εo
Conductor results include cases such as parallel plates and spheres.
Conductors in electrostatic€equilibrium:
€
Electric field inside is zero.
Excess charge resides
€ on the outer surface.
When conductors are in an electric field, induced
charges will appear on the surface(s) of the conductor.
Electric shielding and safety (It’s NOT the rubber tires!)