AP Physics Todays Agenda

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AP PhysicsTodays Agenda

• CHAPTER 16 - ELECTRIC POTENTIAL AND ELECTRIC
  ENERGY CAPACITANCE
• Chp 16 problems 1,5,7,9,13,15,17,19

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OBJECTIVESAfter studying the material
of this chapter the student should be able to

• 1. Write from memory the definitions of electric
  potential and electric potential difference.
• 2. Distinguish between electric potential,
  electric potential energy and electric potential
  difference.
• 3. Draw the electric field pattern and
  equipotential line pattern which exist between
  charged objects
• 4. Determine the magnitude of the potential at a
  point a known distance from a point charge or an
  arrangement of point charges.
• 5. State the relationship between electric
  potential and electric field and determine the
  potential difference between two points a fixed
  distance apart in a region where the electric
  field is uniform.

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OBJECTIVES

• 6. Determine the kinetic energy in both joules
  and electron volts of a charged particle which is
  accelerated through a given potential
  difference.
• 7-9 At a later date
• 7. Explain what is meant by an electric dipole
  and determine the magnitude of the electric
  dipole moment between two point charges.
• 8. Given the dimensions, distance between the
  plates and the dielectric constant of the
  material between the plates, determine the
  magnitude of the capacitance of a parallel plate
  capacitor.
• 9. Given the capacitance, the dielectric
  constant and either the potential difference or
  the charge stored on the plates of a parallel
  plate capacitor, determine the energy and the
  energy density stored in the capacitor.

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KEY TERMS AND PHRASES

• electric potential electric
  dipole moment
• electric potential difference debye
• electric potential energy
  capacitor
• voltage
  farad
• equipotential lines
  microfarad
• electron volt
  picofarad
• electric dipole
  energy density

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ELECTRIC POTENTIAL AND POTENTIAL DIFFERENCE

• The ELECTRIC POTENTIAL at point a (Va) equals the
  electric
  potential energy (PEa)
  per unit
  charge (q)
  placed at that point. V A PE A /q

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The ELECTRIC POTENTIAL DIFFERENCE between two
points (V A) is measured by the work required to
move a unit of electric charge from point b to
point a. Vab Va - Vb Wab/q
The potential difference can also be discussed
in terms of the change in potential energy of a
charge q when it is moved between points a and
b. ?PE PEa - PEb q V., and therefore Vb
?PE/q
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VOLTAGE

• Potential difference is often referred to as
  VOLTAGE.
• Both potential and potential difference are
  scalar quantities which have dimensions of
  Joules/Coulomb.
• The SI unit of electric potential and potential
  difference is the VOLT (V), where I V I J/C.

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Electric Potential and Electric Field
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Electric Potential and Electric Field

• The effects of any charge distribution can be
  described in terms of electric field or in terms
  of electric potential
• The work done by the electric field to move a
  positive charge is WVba q
• The work done by the electric field is also W
  Fd where the force on the positive charge in a
  uniform electric field is FqE and d is the
  distance (parallel to the field lines) between
  points a and b.

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Electric Potential and Electric Field

• W Fdq Vba qEd
• Vba Ed (uniform field)
• E Vba /d (uniform field)
• Equivalent units N/C Nm/Cm J/Cm V/m

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E is the electric field strength in N/C, d is the
distance between points a and b in meters and ?
is the angle between the electric field vector
and the displacement vector.

• If the charged particle is in an electric field
  which is uniform, i.e., constant in magnitude
  and direction, then the potential
  difference is related to the electric field as
  follows Vab E d Cos ?

b
?
Vab
a
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If the electric field is non-uniform, i.e.,
varies in magnitude and direction between points
a and b, then the electric field strength can
only be properly defined over an incremental
distance.
?
b
a
b
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If we consider the x component of the electric
field (Ex), then Ex -? V/ ? x, where ? V is the
change in potential over a very short distance ?
x. The minus sign indicates that E points in the
direction of decreasing V.
Ex -? V/ ? x
b
?
a
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EQUIPOTENTIAL LINES

• EQUIPOTENTIAL LINES are lines along which each
  point is at the same potential. On an
  equipotential surface, each point on the surface
  is at the same potential. The equipotential line
  or surface is perpendicular to the direction of
  the electric field lines at every point. Thus,
  if the electric field pattern is known, it is
  possible to determine the pattern of
  equipotential lines or surfaces,and vice
  versa.

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In the following diagrams, the dashed lines
represent equipotential lines and the solid lines
the electric field lines.
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THE ELECTRON VOLT

• The energy gained by a charged particle which is
  accelerated through a potential difference can
  be expressed in ELECTRON VOLTS (eV) as well as
  joules. Higher amounts of energy can be measured
  in KeV or MeV.
• I eV 1.6 x 10-19 J and I KeV 103eV and I Mev
  106 eV.
• eV is NOT a proper SI Unit. The joules unit
  should really be used when calculating kinetic
  energy changes.

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ELECTRIC POTENTIAL DUE TO A POINT CHARGE

• E kQ/r2 and V Ed (d can be considered to be
  the same as r) therefore V kQ/r
• The electric potential due to a point charge q
  at a distance r from the charge is given by
  V kQ/r (1/4? ? 0 ) Q/r
• Note that the zero of potential is arbitrarily
  taken to be at infinity ( For a negative charge,
  the potential at distance r from the charge is
  less than zero. As r increases, the potential
  increases toward zero, reaching zero at r)
• If more than one point charge is present, the
  potential at a particular point is equal to the
  arithmetic sum of the potential due to each
  charge at the point in question. Sound familiar?

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ELECTRIC DIPOLE

• Two equal point charges q, of opposite sign,
  separated by a distance are called an ELECTRIC
  DIPOLE.
• Since V is equal to the sum of the potentials of
  the individual charges

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ELECTRIC DIPOLE

• If r gtgtl the equation can be simplified. (yeah
  right!)
• ? r ? l cos ?
• Since r gtgt ? r, its contribution to the sum (r
  ? r) can be neglected in the denominator
• Therefore
• Where ? is between 0 and 90 degrees,and V is
  positive.
• Where ? is between 90 and 180 degrees,and V is
  negative
• Notice that the V depends on r2
• As r gets larger, V gets smaller much faster with
  a dipole Why?

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ELECTRIC DIPOLE

• The product Ql is the DIPOLE MOMENT (p) and the
  potential can be written v k p cos ?/r2
  
• The SI unit of the dipole moment (p) is the
  DEBYE, where I debye 3.33 x 10 C m.
• In polar molecules, such as water, the molecule
  is electrically neutral but there is a separation
  of charge in the molecule. Such molecules have
  a net dipole moment.

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CAPACITANCE AND DIELECTRICS
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CAPACITANCE AND DIELECTRICS

• A CAPACITOR stores electric charge and consists
  of two conductors separated by an insulator known
  as a dielectric. The ability of a capacitor to
  store electric charge is referred to as
  CAPACITANCE (C) and is found by the following
  equation C Q/V
• Q is the charge stored in coulombs and V is the
  potential difference between the conducting
  surfaces in volts.
• The SI unit of capacitance is the farad (F),
  where I farad I coulomb/volt (1 F I C/V).
• Typical capacitors have values which range from I
  picofarad (I pF) to 1 microfarad (1 ?F) where
  I pF I x 10-12 F and I ? F I x
  10-6 F

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CAPACITANCE AND DIELECTRICS

• The capacitance of a capacitor depends on the
  physical characteristics of the capacitor as well
  as the insulating material which separates the
  conducting surfaces which store the electric
  charge.
• For a parallel plate capacitor, the capacitance
  is given by C ?0 A/d
  where ?0 is the
  permittivity of free space 8.85 x 1O-12 C2/N
  m2

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CAPACITANCE AND DIELECTRICS

• In most capacitors there is an insulating sheet
  (such as paper or plastic) called a dielectric
  between the plates.
• Dielectrics break down less readily than air and
  allows plates to be placed closer together
  (without charge passing across the gap)
• For a parallel-plate capacitor C K ?0 A/d
  
• ? K ?0 where ? is the permittivity of
  the material.

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DIELECTRICS

• K is the dielectric constant of the insulating
  material between the plates. The constant
  isdimensionless and depends on the material.
  For dry air at 20'C, the constant is 1.0006. E.
  is the permittivity of free space. A is
  the surface area of one side of one plate which
  is opposed by an the
  equal area of the other plate and d is the
  distance between the plates. E is the
  permittivity of the
  material between the plates.