Download An equipotential surface is a surface on which the

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.
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.
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.
The surface of any
conductor is an
equipotential surface
when at equilibrium
under electrostatic
conditions.
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.
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.
From previous equations:
∆V = -W/q0 = -q0E∆s/q0
or ∆V = -E∆s
or E = -∆V/∆s
(The magnitude of E = V/d)
The quantity ∆V/∆s is called
the potential gradient.
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.
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.
The proportion of charge to
voltage in a capacitor is
expressed with a proportionality
constant called the capacitance
C of the capacitor.
q = CV
The unit of capacitance is the
coulomb/volt = farad (F).
One farad, one
coulomb/volt is a huge
capacitance.
Usually smaller amounts
are used in circuits
-6
(microfarad, 1µF =10 F)
-12
(picofarad, pF = 10 F).
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.
A dielectric causes the electric
field between the plates to
decrease. This reduction is
described by the dielectric
constant κ, the ratio of the
electric field strength E0 without
the dielectric to the strength E
inside the dielectric:
κ = E0/E . (unitless)
E = E0/k = V/d
Remember E0 = q/(ε0A),
(CH 18)
so, q/(κε0A) = V/d
Solving for q, gives:
q = (κε0A/d)V, but q = VC,
so:
capacitance C = κε0A/d.
If C0 is the capacitance of
an empty capacitor, the
capacitance of a capacitor with
a dielectric is C = κC0. Since all
dielectrics (except a vacuum)
have a κ that is greater than 1;
the purpose of a dielectric is to
raise the capacitance.
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 κ
of the material?
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,
2
so energy = 1/2 CVV = 1/2 CV .
But V = Ed, and C = κε0A/d,
so:
2
Energy = 1/2 (κε0A/d)(Ed) .
A x d = the volume between
the plates, so:
Energy density =
2
energy/volume = 1/2 κε0E .
This is valid for any electric field strength,
not just between the plates of a capacitor.
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.