Ch. 20 Electric Potential and Electric Potential Energy

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Ch. 20 Electric Potential and Electric Potential
Energy
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Electric Potential Energy

• Electrical potential energy is the energy
  contained in a configuration of charges. Like all
  potential energies, when it goes up the
  configuration is less stable when it goes down,
  the configuration is more stable.
• The unit is the Joule.

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Equation

• DU - W q0Ed
• q0 test charge
• E Electric field
• d - distance

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Electrical potential energy increaseswhen
charges are brought into lessfavorable
configurations
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Electrical potential energy decreases when
charges are brought into more favorable
configurations.
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Work must be done on the charge to increase the
electric potential energy
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• For a positive test charge to be moved upward a
  distance d, the electric force does negative
  work.
• The electric potential energy has increased and U
  is positive (U2 gt U1)

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• If a negative charge is moved upward a distance
  d, the electric force does positive work.
• The change in the electric potential energy U is
  negative (U2 lt U1)

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Electric Potential (V)

• Electric potential is hard to understand, but
  easy to measure.
• We commonly call it voltage, and its unit is
  the Volt.
• 1 V 1 J/C
• Electric potential is easily related to both the
  electric potential energy, and to the electric
  field.

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• The change in potential energy is directly
  related to the change in voltage.
• DU qDV
• DV DU/q
• DU change in electrical potential energy (J)
• q charge moved (C)
• DV potential difference (V)
• All charges will spontaneously go to lower
  potential energies if they are allowed to move.

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• Since all charges try to decrease UE, and DUE
  qDV, this means that spontaneous movement of
  charges result in negative DU.
• DV DU / q
• Positive charges like to DECREASE their potential
  (DV lt 0)
• Negative charges like to INCREASE their
  potential. (DV gt 0)

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• Sample Problem A 3.0 µC charge is moved through
  a potential difference of 640 V. What is its
  potential energy change?

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• Sample Problem A 3.0 µC charge is moved through
  a potential difference of 640 V. What is its
  potential energy change?

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Electrical Potential in Uniform Electric Fields

• The electric potential is related in a simple way
  to a uniform electric field.
• DV -Ed
• DV change in electrical potential (V)
• E Constant electric field strength (N/C or V/m)
• d distance moved (m)

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• Sample Problem An electric field is parallel to
  the x-axis. What is its magnitude and direction
  if the potential difference between x 1.0 m and
  x 2.5 m is found to be 900 V?

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• Sample Problem An electric field is parallel to
  the x-axis. What is its magnitude and direction
  if the potential difference between x 1.0 m and
  x 2.5 m is found to be 900 V?

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• Sample Problem If a proton is accelerated
  through a potential difference of 2.000 V, what
  is its change in potential energy?
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• How fast will this proton be moving if it started
  at rest?

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• Sample Problem A proton at rest is released in a
  uniform electric field. What potential difference
  must it move through in order to acquire a speed
  of 0.20 c?

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Electric Potential Energy forSpherical Charges

• Electric potential energy is a scalar, like all
  forms of energy.
• U kq1q2/r
• U electrical potential energy (J)
• k 8.99 109 N m2 / C2
• q1, q2 charges (C)
• r distance between centers (m)
• This formula only works for spherical charges or
  point charges.

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Absolute Electric Potential(spherical)

• For a spherical or point charge, the electric
  potential can be calculated by the following
• Formula V kq/r
• V potential (V)
• k 8.99 x 109 N m2/C2
• q charge (C)
• r distance from the charge (m)
• Remember, k 1/(4peo)

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Electric Field and Electric Potential

• E - V / d
• Two things about E and V
• The electric field points in the direction of
  decreasing electric potential.
• The electric field is always perpendicular to the
  equipotential surface.

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20-4 Equipotential Surfaces and the Electric Field
For two point charges
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Equipotential Surfaces and the Electric Field
An ideal conductor is an equipotential surface.
Therefore, if two conductors are at the same
potential, the one that is more curved will have
a larger electric field around it. This is also
true for different parts of the same conductor.
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Equipotential Surfaces and the Electric Field
There are electric fields inside the human body
the body is not a perfect conductor, so there are
also potential differences.
An electrocardiograph plots the hearts
electrical activity.
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Equipotential Surfaces and the Electric Field
An electroencephalograph measures the electrical
activity of the brain
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Capacitor

• Named for the capacity to store electric charge
  and energy.
• A capacitor is two conducting plates separated by
  a finite distance

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The capacitance relates the charge to the
potential difference
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• Sample Problem A 0.75 F capacitor is charged to
  a voltage of 16 volts. What is the magnitude of
  the charge on each plate of the capacitor?

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• Sample Problem A 0.75 mF capacitor is charged to
  a voltage of 16 volts. What is the magnitude of
  the charge on each plate of the capacitor?
• V 16 V, C 0.75 mF 0.75 x 10-6 F
• Q ?
• C Q/V or Q CV
• Q (0.75 x 10-6)(16)
• Q 1.2 x 10-5 C

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A simple type of capacitor is the parallel-plate
capacitor. It consists of two plates of area A
separated by a distance d.
By calculating the electric field created by the
charges Q, we find that the capacitance of a
parallel-plate capacitor is
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The general properties of a parallel-plate
capacitor that the capacitance increases as the
plates become larger and decreases as the
separation increases are common to all
capacitors.
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Capacitor Geometry

• The capacitance of a capacitor depends on HOW you
  make it.

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• Sample Problem What is the AREA of a 1 F
  capacitor that has a plate separation of 1 mm?
• C 1 F, d 1 mm 0.001 m,
  eo 8.85 x 10-12 C2/(Nm2)

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Is this a practical capacitor to build?
NO! How can you build this then?
The answer lies in REDUCING the AREA. But you
must have a CAPACITANCE of 1 F. How can you keep
the capacitance at 1 F and reduce the Area at the
same time?
1.13 x 108 m2
Add a DIELECTRIC!!!
10629 m
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A dielectric is an insulator when placed between
the plates of a capacitor it gives a lower
potential difference with the same charge, due to
the polarization of the material. This increases
the capacitance.
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Dielectric

• Remember, the dielectric is an insulating
  material placed between the conductors to help
  store the charge. In the previous example we
  assumed there was NO dielectric and thus a vacuum
  between the plates.

All insulating materials have a dielectric
constant associated with it. Here now you can
reduce the AREA and use a LARGE dielectric to
establish the capacitance at 1 F.
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• Sample Problem A parallel plate capacitor is
  constructed with plate of an area of 0.028 m2 and
  a separation of 0.55 mm. Find the magnitude of
  the charge of this capacitor when the potential
  difference between the plate is 20.1 V.

A 0.028 m2 d 0.55 mm 0.00055 m,
V 20.1 V Q ? Q CV
C eo A/d C(8.85 x 10 -12)(0.028)
/(0.00055) C 4.51 x 10-10 F
Q (4.51 x 10-10 )(20.1) Q 9.06 x 10-9 C
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The polarization of the dielectric results in a
lower electric field within it the new field is
given by dividing the original field by the
dielectric constant ?
Therefore, the capacitance becomes
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The dielectric constant is a property of the
material here are some examples
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Using MORE than 1 capacitor

• Lets say you decide that 1 capacitor will not be
  enough to build what you need to build. You may
  need to use more than 1. There are 2 basic ways
  to assemble them together
• Series One after another
• Parallel between a set of junctions and
  parallel to each other.

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Capacitors in Series

• Capacitors in series each charge each other by
  INDUCTION. So they each have the SAME charge. The
  electric potential on the other hand is divided
  up amongst them. In other words, the sum of the
  individual voltages will equal the total voltage
  of the battery or power source.

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Capacitors in Parallel

• In a parallel configuration, the voltage is the
  same because ALL THREE capacitors touch BOTH ends
  of the battery. As a result, they split up the
  charge amongst them.

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Capacitors STORE energy

• Anytime you have a situation where energy is
  STORED it is called POTENTIAL. In this case we
  have capacitor potential energy, Uc

Suppose we plot a V vs. Q graph. If we wanted to
find the AREA we would MULTIPLY the 2 variables
according to the equation for Area. A
bh When we do this we get Area VQ Lets do a
unit check! Voltage Joules/Coulomb Charge
Coulombs Area
ENERGY
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Potential Energy of a Capacitor
Since the AREA under the line is a triangle, the
ENERGY(area) 1/2VQ
This energy or area is referred as the potential
energy stored inside a capacitor. Note The
slope of the line is the inverse of the
capacitance.
most common form
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• Sample Problem In a typical defibrillator, a 175
  mF, is charged until the potential difference
  between the plates is 2240 V. A.) What is the
  charge on each plate?
• V 2240 V, C 175 mF 175 x 10-6 F
• Q ?
• Q CV
• Q (175 x 10-6)(2240)
• Q 0.392 C

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• B.) Find the energy stored in the charged up
  defibrillator.
• U ?
• Since you now know Q, C, V. You may use any of
  the 3 equations to find U.
• U ½ CV2 U ½ QV U Q2/(2C)
• U ½ (0.392)(2240)
• U 439 J

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• The energy stored in a capacitor can be put to a
  number of uses a camera flash a cardiac
  defibrillator and others. In addition,
  capacitors form an essential part of most
  electrical devices used today.
• If we divide the stored energy by the volume of
  the capacitor, we find the energy per unit
  volume this result is valid for any electric
  field

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If the electric field in a dielectric becomes too
large, it can tear the electrons off the atoms,
thereby enabling the material to conduct.
This is called dielectric breakdown the field at
which this happens is called the dielectric
strength.