Ch. 21:
Coulomb’s Law:
= force between
two point charges (in a vacuum).
Electric field
:
Electric field of a point charge
:
REMEMBER:
Electric field of a ring of charge
:
(for a ring with symmetry on x
axis, centered in yz plane).
Field of a finite line of charge:
With charge density
,
=Q/2a:
λ λ
thus
for infinite line of charge
Field for finite, uniformly charged disk
:
for infinite charged disk
For two oppositely charged, infinite sheets, E inside is
2E, outside either sheet is 0.
Dipole = pair of pt. charges with equal magnitude,
opposite sign
p=qd ->
p
=q
d
(p = dipole moment)
=pEsin ->
τ
τ
=
p
x
E,
U=-
p*E
Potential energy U at its lowest when dipole is in
stable equilibrium. U = -pEcos
Ch 22 – Gauss’s Law, Eflux:
e =
E cos dA = E
Φ
∫
φ
┴
dA =
E
.
d
A
=
Q
encl
/
ε
o
=
Gauss’s Law
Single pt charge, E = (1/4
πε
o
)(q/r
2
)
Charge on surface of conducting sphere,
E
= (1/4
πε
o
)
(q/r
2
)
Inside sphere = 0
Infinite wire, E = (1/2
πε
o
)(
/r)
λ
Infinite conducting cylinder, E = (1/2
πε
o
)(
/r)
λ
Inside = 0
Solid insulating sphere, Q distributed uniformly
throughout, E
= (1/4
πε
o
)(Q/r
2
)
Inside sphere E = (1/4
πε
o
)(Qr/R
3
)
Infinite sheet with uniform charge, E =
/2
σ ε
o
2 oppositely charged conducting plates, E =
/
σ ε
o
Ch 23 – Potential energy, electric potential:
W
a
b
= U
a
- U
b
=-(U
b
-U
a
)
U=Fd=q
0
Ed
K
b
+U
b
=K
a
+U
a
U = (1/4
πε
o
)(qq
0
/r) = (q
0
/4
πε
o
)(q
1
/r
1
+ q
2
/r
2
+ …)
Equi triangle: U = (1/4
πε
0
)(1/r)(q
1
q
2
+q
2
q
3
+q
1
q
3
)
V = U/q
0
= (1/4
πε
o
)(q/r) or (q
0
/4
πε
o
)(q
1
/r
1
+ q
2
/r
2
+ …)
V = (1/4
πε
o
)
(dq/r)
∫
Va – Vb =
∫
E
d
l
=
E cos dl
∫
φ
E
= -(dV/dx
i
+ dV/dy
j
+ dV/dz
k
)
V for a
point outside a sphere
(r away):
V for
inf. line charge or charged conducting cyl
.:
V in
oppositely charged plates
(y-axis up is
positive): V=Ey,
(a is top,
+plate, b is bottom, -plate)
Charge density
for above:
V for
rod of length 2a
:
V for
point x from center of ring of charge
:
Ch 24 – Capacitance, Dielectrics:
C = Q/V
ab