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Transcript
Text sections 25.1, 25.2, 25.4
• Potential Energy and Electric Potential
• Field and Potential
• Equipotential surfaces
Practice problems:
Chapter 25, problems 1, 5, 9, 32, 65
(Potential energy per unit charge)
A “test charge” q is moved
from A to B in a field:
B
E
ds
q +
A
Find: work done by the field.
1
Recall…
or
The work is proportional to the charge.
The electric force is conservative. Define an
electrostatic potential energy, U, such that:
When the field does work on the test charge,
electrostatic potential energy is converted to
other forms of energy.
so we introduce
Electric Potential:
or
Units: 1 volt = 1 joule/coulomb (V)
•  V is a SCALAR field
• V is produced by other charges Q
• V is a little arbitrary; we can choose to set V=0 at
any position (often at “infinity”)
2
•  A unit of energy
1 eV = e × (1 volt) ≈ 1.609×10-19 J
Find
to accelerate electrons to 107 m/s.
and
V2
V1
-
-
v1 ≈ 0
v2 = 1×107 m/s
3
V2
V1
-
-
Solution:
Since K1 = 0…
OR
4
B
q
A
+
and
-ΔV
s cosθ
d||
E
V2
(low)
V1
(high)
Uniform E: ΔV = In general:
Ed||
( Note Units:
1 N/C = 1 volt/metre)
5
E
ds
q +
work in infinitesimal displacement,
dW = qE⋅ds = -qdV
so in general,
dV = - E⋅ds
•  (Imaginary) surfaces on which V has some
uniform value
•  Equipotential surfaces are ⊥ field lines
•  A conductor is always an equipotential (if no
current)
•  Closely spaced where |E| is large; widely spaced
where |E| is weak.
6
battery
2 mm
E = 50 000 N/C between the plates (uniform)
a)  Find battery voltage
b)  Sketch a few equipotentials
E = 50 000 N/C between
the plates (uniform)
battery
2 mm
The battery voltage is
A)  50 000 volts
B)  100 volts
C)  25 volts
D)  1.5 volts
7
battery
2 mm
The equipotentials between the plates are
A)  vertical planes
B)  horizontal planes
C)  vertical lines
D)  spherical
wire
metal plate
------------+ + + + + + + + + + + + + + charged plastic slab
- - - - - - - - - - - - - metal plate
a) Which plate is at the higher potential?
b) Which plate has the larger (negative) charge?
8
-------------
-q
+ + + + + + + + + + + + + + +2q
-------------q
The wire is removed, and the top plate is lifted up.
Which plate is at the higher potential now?
a)  the upper plate
b)  the lower plate
c) they are at the same potential
V2
q,m
gravity
h = 1.0 mm
V1
Oil droplet , with charge q = +5e (8×10-19 C)
and mass m = 5×10-15 kg)
Find: Potential Difference V2-V1 for equilibrium.
answer: |ΔV| = 61 volts
9