Summary Lecture 4
Mechanics
Electricity
Energy is conserved
Only differences in Potential Energy: PE
+
PE = mgh
PE = ???
= Mass x “Potential”
= Charge x “Potential”
=qV
Electric Potential V = PE/q
Potential Difference V = PE/q
[Units]: 1 Volt: 1 V = 1 J/C
Positive probe moves to LOWER potential.
Negative probe moves to HIGHER potential.
Special Case: Parallel Plates
d
Two charged plates, distance d
E = constant
+
=> F = qE is constant
-
Move positive charge closer to positive plate.
Work = PE
Fd
= V q
qEd = V q
V = E d
(for constant E)
PE = q V = q E d
Special Case: Point Charge
Positive charge Q generates an electric field:
E = k Q/r2
Force on a probe charge q
F = k (Qq)/ r2
BUT force is NOT constant
Move positive charge closer to positive charge.
A small step  at a time !
rfinal
+
rinitial
+
Work = PE
F1 + F2+ F3 + F4 ...
Calculus
= V q
V = k Q/rfinal - k Q/rintial
PE = q V = k (qQ)/rfinal - k (qQ)/rintial
For rintial = infinity: Potential of Sphere V = kQ/r
Equipotential
Surface
Multiple charges:
Electric field + forces: Vector add.
Potential:
Normal add.
V1 (A) = kQ1/r1 = 9000 V
V2 (A) = kQ2/r
/ 2 = -9000
9000 V
Vtot (A) = V1 (A) + V2 (A)
=0V
A
2m
2 C
(Q1)
-2 C
(Q2)
Electrostatics
General
Concept
Special Cases
Point Charge
Parallel Plates
Force F
Coulomb’s Law
F = qE
or
F = k (Q1Q2)/r2
(vector)
Like charges repel
Unlike charges attract
Electric Field E = k Q
Q/r2
E = F/q
(vector in direction of
force on (+) charge)
Potential
difference
V = PE/q
F = qE
F = q V/d
E is constant
E = V/d
V=kQ/rb-kQ/ra
( V = kQ/r)
V = Ed
PE=k(qQ)/rbk(qQ)/ra
PE = Ed q
(scalar)
Potential
Energy
gy
PE = V q
Use your
Potential
+
Pinewood Derby (for Physicists)
q=-2x10
q
2x10-4C
h = 1m
+
Q 0 3C
Q=0.3C
Solution:
Use energy conservation
mgh + PEel(3.3 m) = m/2 v2 + PEel(0.3 m)
m/2 v2 = mgh + PEel(3.3 m) - PEel(0.3 m)
With
mgh = 0.5 kg * 9.8 m/s2 * 1 m = 4.9 J
PEel(3.3
(3 3 m)
= kqQ/r
= k (-2x10-4C) 0.3C/3.3m
= -1.64 x 105 J
PEel(0.3 m)
= kqQ/r
= k ((-2x10
2 10-44C) 0.3C/0.3m
0 3C/0 3
= -1.8 x 106 J
We find
m/2 v2 = 1.63 x 106 J
v = 2553 m/s (>5000 mph Oops!)