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PH 202-5E Fall 2005
Electrostatic Potential and Energy
Lectures 5-7
Chapter 19(Cutnell & Johnson, Physics 6th edition)
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Electrostatic Potential and Energy
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Uniform electric field in the space between two charged parallel plates
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Electrostatic Potential V at a given point is the electric potential energy of a small test charge q situated at that point divided by the charge itself
Neither the potential V nor the potential energy EPE can be determined in an absolute sense, because only the differences ∆V and ∆EPE are measurable in terms of the work WAB.
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The electric potential difference created by a point chargeThe positive test charge +qoexperiences a repulsive force F due to the positive point charge +q. As a result, work is done by this force when the test charge moves from A to B. consequently, the electric potential is higher (uphill) at A and lower (downhill) at B.
WAB=kqqo/rA-kqqo/rB
VB-VA=-WAB/q=kq/rB -kq/rA
for rB=∞ kq/rB=0 ⇒VB=0
⇒VA= kq/rA or V=kq/r
The symbol V does not refer to the potential in any absolute sense. Rather,
V =kq/r stands for the amount by which the potential at a distance r from a point charge differs from te potential at an infinite distance away. In other words, V refers to a potential difference with the arbitrary assumption that the potential at infinity is zero.
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Example. The potential of a point charge for a zero reference potential at infinity
A point charge of q=4.0x10-8C creates a potential at a spot 1.2 m away.
The potential is (a) V=kq/r=
=(8.99x109)(+4.0x10-8)/1.2=+300V when the charge is positive
and (b) -300V when the charge is negative
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The acceleration of positive and negative charges
A positive charge accelerates from a region of higher electric potential toward a region of lower electric potential
A negative charge accelerates from a region of lower electric potential toward a region of higher electric potential
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The electric potential energy of a point charge q for non-uniform electric field
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Electrostatic Potential of a point charge
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One electron volt is the magnitude of the amount by which the potential energy of an electron changes when the electron moves through the potential difference of 1 volt
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A headlight connected to a 12-V battery
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-2.3x10-18 J
-6.5x10-19 J
done by the electric force
Work to be done against the electric force = +10 eV
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Equipotential surface for a very large sheet with a uniform distribution of charge
Definition: Equipotential surface – a mathematical surface on which the electrostatic potential has a fixed constant value
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Equipotential surfaces for a positive point charge.The equipotentials are concentric spheres. Points at the same distance
from the central charge are at the same potential
rqqU
o
'4
1 ⋅⋅=
πε
rq
qUV
o
⋅==πε41
'
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Properties of the equipotential surfaces and some useful conclusions
but it is wrong V1=V2
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Energy of a system of charged conductors
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1.0 mm
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Capacitance
A large value of C implies that a large amount of charge can be stored at low voltage.
28V
QC∆
=
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Capacitance of a parallel plate capacitor
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Potential energy in capacitor
signal.
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Dielectrics
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