An equipotential surface is a surface on which the electric potential is the same everywhere. Since the potential at a distance r from an isolated point charge is V = kq/r, the potential is the same wherever r is the same.

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An equipotential surface is a surface on which
the electric potential is the same everywhere.
Since the potential at a distance r from an
isolated point charge is V kq/r, the potential
is the same wherever r is the same.
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The net electric force does no work as a charge
moves on an equipotential surface. The net
electric force does do work as a charge moves
between equipotential surfaces.
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The electric field created by any group of
charges (or a single charge) is everywhere
perpendicular to the associated equipotential
surfaces and points in the direction of
decreasing potential.
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The surface of any conductor is an equipotential
surface when at equilibrium under electrostatic
conditions.
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Actually, since the electric field is zero
everywhere inside a conductor whose charges are
in equilibrium, the entire conductor can be
regarded as an equipotential volume.
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When a charge is moved between the plates of a
parallel plate capacitor, the force applied is
the product of the charge and the electric field
F q0E. The work done is W F?s q0E?s.
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From previous equations?V -W/q0
-q0E?s/q0or ?V -E?sor E -?V/?s (The
magnitude of E V/d)The quantity ?V/?s is
called the potential gradient.
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Ex. 9 - The plates of a capacitor are separated
by a distance of 0.032 m, and the potential
difference between them is ?V VB - VA -64V.
Two equipotential surfaces between the plates
have a potential difference of -3.0 V. Find the
spacing between the two equipotential surfaces.
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A capacitor is composed of any two conductors of
any shape placed near each other without
touching. The region between the conductors is
often filled with a material called a dielectric.
A capacitor stores electric charge.
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The proportion of charge to voltage in a
capacitor is expressed with a proportionality
constant called the capacitance C of the
capacitor. q CVThe unit of capacitance
is the coulomb/volt farad (F).
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One farad, one coulomb/volt is a huge
capacitance. Usually smaller amounts are used in
circuits (microfarad, 1µF 10-6 F) (picofarad,
pF 10-12 F).
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Capacitance describes the ability of a capacity
to store charge. RAM chips contain millions of
capacitors. A charged capacitor is a 1, an
uncharged capacitor is a 0 in the binary
system.
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A dielectric causes the electric field between
the plates to decrease. This reduction is
described by the dielectric constant ?, the ratio
of the electric field strength E0 without the
dielectric to the strength E inside the
dielectric ? E0/E . (unitless)
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E E0/k V/d Remember E0 q/(e0A), (CH
18)so, q/(?e0A) V/dSolving for q, givesq
(?e0A/d)V, but q VC, socapacitance C ?e0A/d.
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If C0 is the capacitance of an empty capacitor,
the capacitance of a capacitor with a dielectric
is C ?C0. Since all dielectrics (except a
vacuum) have a ? that is greater than 1 the
purpose of a dielectric is to raise the
capacitance.
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Ex. 10 - The capacitance of an empty capacitor is
1.2 µF. The capacitor is connected to a 12-V
battery and charged up. With the capacitor
connected to the battery, a slab of dielectric
material is inserted between the plates. As a
result, 2.6 x 10-5 C of additional charge flows
from one plate, through the battery, and on to
the other plate. What is the dielectric constant
? of the material?
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A capacitor is a device for storing charge, but
also energy. The total work done by a battery in
charging a capacitor is 1/2 qV. This is stored in
the capacitor as electrical potential energy, EPE
1/2 qV. q CV, so energy 1/2 CVV 1/2 CV2.
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But V Ed, and C ?e0A/d, soEnergy 1/2
(?e0A/d)(Ed)2.A x d the volume between the
plates, soEnergy density energy/volume 1/2
?e0E2.This is valid for any electric field
strength, not just between the plates of a
capacitor.
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Capacitors are used to build up a large charge
with a high potential which can then be released
when needed. Capacitors such as this are used in
electronic flashes in cameras, tazers and in
defibrillators.
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