Charge

1
Charge

• Comes in and
• Is quantized
• elementary charge, e, is charge on 1 electron or
  1 proton
• e 1.602 ? 10-19 Coulombs
• Is conserved
• total charge remains constant

2
Coulombs Law

• F kq1q2/r2
• k 8.99 ? 109 N m2 / C2
• q1, q2 are charges (C)
• r2 is distance between the charges (m)
• F is force (N)
• Applies directly to spherically symmetric charges

3
Spherical Electric Fields
force
field
4
Why use fields?

• Forces exist only when two or more particles are
  present.
• Fields exist even if no force is present.
• The field of one particle only can be calculated.

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Field around charge
Positive charges accelerate in direction of lines
of force
Negative charges accelerate in opposite direction
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Field around - charge
Positive charges follow lines of force
Negative charges go in opposite direction
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For any electric field

• F Eq
• F Force in N
• E Field in N/C
• q Charge in C

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Principle of Superposition
When more than one charge contributes to the
electric field, the resultant electric field is
the vector sum of the electric fields produced by
the various charges.
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Field around dipole
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Caution

• Electric field lines are NOT VECTORS, but may be
  used to derive the direction of electric field
  vectors at given points.
• The resulting vector gives the direction of the
  electric force on a positive charge placed in the
  field.

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Field Vectors
12
Electric Potential
potential energy
potential
(for spherically symmetric charges)
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Electrical Potential

• ?V -Ed
• ?V change in electrical potential (V)
• E Constant electric field strength (N/m or V/m)
• d distance moved (m)

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Electrical Potential Energy

• ?U q?V
• ?U change in electrical potential energy (J)
• q charge moved (C)
• ?V potential difference (V)

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Electrical Potentialand Potential Energy
Are scalars!
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Potential Difference

• Positive charges like to DECREASE their
  potential.
• (DV lt 0)
• Negative charges like to INCREASE their
  potential.
• (DV gt 0)

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Announcements 12/22/2015

• Lunch Bunch Wednesday
• Graded quiz tomorrow
• Exam Friday

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Potential surfaces
positive
negative
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Equipotential surfaces
high
low
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Today...

• More with electric potential and potential energy.

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Definition Capacitor

• Consists of two plates in close proximity.
• When charged, there is a voltage across the
  plates, and they bear equal and opposite charges.
• Stores electrical energy.

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Capacitance

• C q / DV
• C capacitance in Farads (F)
• q charge (on positive plate) in Coulombs (C)
• V potential difference between plates in Volts
  (V)

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Energy in a Capacitor

• UE ½ C (DV)2
• U electrical potential energy (J)
• C capacitance in (F)
• V potential difference between plates (V)

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Capacitance of parallel plate capacitor

• C ke?0A/d
• C capacitance (F)
• ke dielectric constant of filling
• ?0 permittivity (8.85 x 10-12 F/m)
• A plate area (m2)
• d distance between plates(m)

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Parallel Plate Capacitor
dielectric
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Cylindrical Capacitor
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Problem 2
Calculate the force on the 4.0 ?C charge due to
the other two charges.
4 ?C
60o
60o
1 ?C
1 ?C
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Problem 3
Calculate the mass of ball B, which is suspended
in midair.
q 1.50 nC
A
R 1.3 m
q -0.50 nC
B
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Problem 2
Two 5.0 ?C positive point charges are 1.0 m
apart. What is the magnitude and direction of the
electric field at a point halfway between them?
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Problem 4
Calculate the magnitude of the charge on each
ball, presuming they are equally charged.
40o
1.0 m
1.0 m
A
B
0.10 kg
0.10 kg