Physics 114

1
Electric potential,Systems of charges

• Physics 114

2
Concepts

• Primary concepts
• Electric potential
• Electric energy
• capacitance
• Secondary concepts
• Equipotentials
• Electonvolt

3
Potential electric energy
High PE
High PE
Low PE
Low PE

• Just like gravity electric force can do work
• work does not depend on the path
• it depends only on the initial and final position
  
• ? there is a potential energy associated with
  electric field.

4
Electric potential

• PE/q is a property of the field itself called
  electric potential V

5
Electric potential

• V electric potential is the potential energy of
  a positive test charge in electric field, divided
  by the magnitude of this charge q.
• Electric potential is a scalar (so much nicer!).
• Electric potential is measured in Volts (VJ/C).
• Potential difference between two points DVVb-Va
  is often called voltage.

6
Charges in electric fields

• Econst
• Force on charge q
• FqE
• Work done by the field to move this charge
• WFddqE
• WPEa-PEbqVa-qVb-qDV
• d EDV
• E DV/d, points from high potential to low
• Sometimes electric field is measured in V/m N/C

b

a
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Non-uniform electric field

8
Determine E from V

• Think ski slopes
• If V depends on one coordinate x
• E is directed along x from high V to low
• If V depends on x,y,z

9
Electric field and potential in conductors

• E0 in good conductors in the static situation.
• E is perpendicular to the surface of conductor.
• Metal hollow boxes are used to shield electric
  fields.
• When charges are not moving (!!) conductor is
  entirely at the same potential.

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Electronvolt

• Energy that one electron gains when being
  accelerated over 1V potential difference is
  called electronvolt eV
• 1eV1.6x10-19C 1V 1.6x10-19J
• Yet another unit to measure energy,
• Commonly used in atomic and particle physics.

11
Equipontentials

• Equipotentials
• are surfaces at the same potential
• are always perpendicular to field lines
• Never cross
• Their density represents the strength of the
  electric field
• Potential is higher at points closer to positive
  charge

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Potential of a point charge

• Potential V of electric field created by a point
  charge Q at a radius r is
• Qgt0 ? Vgt0
• Qlt0 ? Vlt0
• Do not forget the signs!
• Potential goes to 0 at infinity.
• Equipotentials of a point charge are concentric
  spheres.

13
Superposition of fields

• Principle of superposition
• Net potential created by a system of charges is a
  scalar (!) sum of potentials created by
  individual charges

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1
2
Potential is a scalar ? no direction to worry
about, But signs are important.
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Work to move a charge

• How much work has to be done by an external force
  to move a charge
• q1.5 mC
• from point a to point b?
• Work-energy principle

30cm

20cm
15cm
25cm
-

Q110mC
Q2-20mC
15
Capacitance

• Two parallel plates are called a capacitor. When
  capacitor is connected to a battery plates will
  charge up.

Note net charge 0

• C coefficient, called capacitance, property of
  the capacitor.
• Capacitance is measured in Farad (FC/V)

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Electric field in a capacitor

• Econst
• E V/d
• points from high potential to low
• When V is fixed (same battery), E depends only on
  the d.
• Potential
• High next to plate
• Low next to - plate

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Capacitance

• Capacitance depends on the geometry of a capacitor

• e0 8.85. 10-12 C2/N m2-
• permittivity of free space
• A area of plates (m2)
• Same sign charges want to spread out to hold
  more charge need large area
• d distance between plates (m)
• Opposite sign charges hold each other,
  attraction is stronger for shorter d

A
d
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Dielectrics

• Put non-conductive material (dielectric) between
  plates
• Can hold more charge ? capacitance increases

• K(gt1) dielectric constant

19
Charging up a capacitor

• Find the work needed to charge a capacitor C to
  voltage V
• Take small charge dq and move it across the
  capacitor, which is at voltage V at this moment
• dWVdq

20
Energy storage

• Work to charge a capacitor potential energy
  stored in the capacitor

• To use the right formula, watch what is kept
  constant
• Vconst if C connected to a battery
• Qconst - if C disconnected

21
Inserting dielectric

• Capacitor is connected to a battery, supplying
  voltage V. How will the energy stored in the
  capacitor change if we insert a dielectric (K2)?
• C?KC2C capacitance increases

V stays const same battery
Q changes
22
Inserting dielectric

• Capacitor is charged to charge Q and disconnected
  from a battery. How will the energy stored in the
  capacitor change if we insert a dielectric (K2)?
• C?KC2C capacitance increases

V can change
Q stays const charge conservation
23
Inserting dielectric
Disconnected battery energy decreases Dielectri
c will be sucked in
Connected battery energy increases Dielectric
will be pushed out
24
Test problem

• Between two very large oppositely charged
  parallel plates at which of the three locations
  A, B and C electric potential is the greatest?
• A A
• B B
• C C
• D Equal at all three locations.

25
E near metal sphere

• Find the largest charge Q that a conductive
  sphere radius r1cm can hold.
• Air breakdown E3x106V/m

Larger spheres can hold more charge
26
Test problem

• What is wrong with this picture?
• A Equipotentials must be parallel to field lines
• B Field lines cannot go to infinity
• C Some field lines point away from the negative
  charge
• D Equipotentials cannot be closed