new topic - george washington university
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PHYS 1022: Chap. 29, Pg 3
Topics: • Electric Potential Energy • The Potential Energy of Point Charges • The Potential Energy of a Dipole
PHYS 1022: Chap. 29, Pg 4
Define potential energy function U via the work done by a conservative force F in the following way:
The work done by a conservative force is equal to the decrease in the potential energy function.
Conservative force Work done by a conservative force does not depend on the path. It only
depends on the initial and final positions.
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PHYS 1022: Chap. 29, Pg 5
Gravity Electric
PHYS 1022: Chap. 29, Pg 6
A negative charge is moved from a to b in a uniform electric field as shown. What happens to the potential energy of the charge?
1) increase 2) decrease 3) stays the same
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PHYS 1022: Chap. 29, Pg 7
+ + + + + +
- - - - - -
+
-
+ + + + + +
- - - - - -
PHYS 1022: Chap. 29, Pg 8
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PHYS 1022: Chap. 29, Pg 9
PHYS 1022: Chap. 29, Pg 10
It depends on the sign of the charges.
Relative to what point is this potential energy defined?
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PHYS 1022: Chap. 29, Pg 11
For a pair of charges
For a system of 3 charges
Generalization to N charges
Avoid double-counting. Watch for sign of charges.
q1
q3
q2
r13
r12
r23
Physical meaning of U: the total work done by us to assemble the charges from infinity to the present configuration.
PHYS 1022: Chap. 29, Pg 12
Which group of charges took more work to bring together from a very large distance
apart ?
+1 +2 d
+1
+1
+1
d d
d
1) Case a 2) Case b 3) Both the same
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PHYS 1022: Chap. 29, Pg 15
Initially the inner shell has a net charge +q, and the outer shell has no net charge. How much work must be done to add –q of charge to the outer shell?
+q
PHYS 1022: Chap. 29, Pg 16
The potential energy of an electric dipole p in a uniform electric field E is
The potential energy is minimum at φ = 0° where the dipole is
aligned with the electric field.
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PHYS 1022: Chap. 29, Pg 17
Rank in order, from most positive to most negative, the potential energies U1 to U6 of these six electric dipoles in a uniform electric field.
PHYS 1022: Chap. 29, Pg 18 New Topic
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PHYS 1022: Chap. 29, Pg 19
Definition: potential is defined as potential energy per unit charge: SI unit: volt. 1 V = 1 J/C
For example: the potential energy between two point charges
q q0 r
Therefore, the potential of point charge q is
For a system of point charges:
Potential is a scalar. There’s no direction to worry about. But you do have to watch the sign of the charges.
(algebraic sum)
PHYS 1022: Chap. 29, Pg 20
. P
r
Q
Relative to which point is this potential defined? infinity