-Potential Energy of Multiple Charges -Finding the Electric Field from the Electric Potential

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-Potential Energy of Multiple Charges-Finding
the Electric Field from the Electric Potential

• AP Physics C
• Mrs. Coyle

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The Potential Energy of Point Charges

• Consider two point charges, q1 and q2, separated
  by a distance r. The electric potential energy is
  
• This is the energy of the system, not the energy
  of just q1 or q2.
• Note that the potential energy of two charged
  particles approaches zero as r ?

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Assume the sphere is a point charge. Apply
conservation of energy. Ki Ui Kf Uf
Ans 1.86 x 107 m/s
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Potential Energy,U, of Multiple Charges

• If the two charges are the same sign, U is
  positive and work must be done to bring the
  charges together
• If the two charges have opposite signs, U is
  negative and work is done to keep the charges
  apart

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U with Multiple Charges, final

• If there are more than two charges, then find U
  for each pair of charges and add them
• For three charges
• The result is independent of the order of the
  charges

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Finding E From V

• Assume, to start, that E has only an x component
• Similar statements would apply to the y and z
  components
• Equipotential surfaces must always be
  perpendicular to the electric field lines passing
  through them

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E and V for an Infinite Sheet of Charge

• The equipotential lines are the dashed blue lines
• The electric field lines are the brown lines
• The equipotential lines are everywhere
  perpendicular to the field lines

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E and V for a Point Charge

• The equipotential lines are the dashed blue lines
• The electric field lines are the brown lines
• The equipotential lines are everywhere
  perpendicular to the field lines

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E and V for a Dipole

• The equipotential lines are the dashed blue lines
• The electric field lines are the brown lines
• The equipotential lines are everywhere
  perpendicular to the field lines

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Equipotential Lines

• Simulation of Field with Equipotential Lines
• http//glencoe.mcgraw-hill.com/sites/0078458137/st
  udent_view0/chapter21/electric_fields_applet.html

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Electric Field from Potential, General

• In general, the electric potential is a function
  of all three dimensions
• Given V (x, y, z) you can find Ex, Ey and Ez as
  partial derivatives

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Why are equipotentials always perpendicular to
the electric field lines?

• When a test charge has a displacement, ds, along
  an equipotential surface dV 0
• dV -Eds0
• So E must be perpendicular to to the displacement
  along the equipotential surface.
• Note that no work is done to move a test charge
  along an equipotential surface.

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Ex 25.4 Electric Potential and Electric Field Due
to a Dipole
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Ex 25.4 Electric Potential and Electric Field Due
to a Dipole

• An electric dipole consists of two charges of
  equal magnitude and opposite sign separated by a
  distance 2a. The dipole is along the x-axis and
  is centered at the origin.
• a) Calculate the electric potential at P.
• b) Calculate V ans Ex at a point far from the
  dipole.
• c)Calculate V and Ex if point P is located
  anywhere between the two charges.

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a) Calculate the electric potential at P.
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b) Calculate V ans Ex at a point far from the
dipole.
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c)Calculate V and Ex if point P is located
anywhere between the two charges.
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If point P is located to the left of the negative
charge, what would be the potential?
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Quick Quiz 25.8
In a certain region of space, the electric
potential is zero everywhere along the x axis.
From this we can conclude that the x component of
the electric field in this region is (a) zero
(b) in the x direction (c) in the x direction.
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Quick Quiz 25.8
Answer (a). If the potential is constant (zero
in this case), its derivative along this
direction is zero.
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Quick Quiz 25.9
Answer (b). If the electric field is zero, there
is no change in the electric potential and it
must be constant. This constant value could be
zero but does not have to be zero.
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Quick Quiz 25.9
In a certain region of space, the electric field
is zero. From this we can conclude that the
electric potential in this region is (a) zero
(b) constant (c) positive (d) negative