Announcements

1
Announcements

• Homework
• Webassign HW due on SUNDAY at 1159pm
• No Hand-in Homework
• Test 1
• Feb 17th, 6-730 pm
• Location SMG 105
• Chapters 21-24
• Practice Exams posted on WebCT
• Review Sessions by discussion TFs
• Friday 3-5pm in SCI 115 (Eric Pinnick)
• 5-7 pm in CAS 313 (Maggie
  Geppert)

2
Summary Electric Potential

• Electric Potential
• Reference point V0 at an infinite distance
  (r??)
• Electric field lines point in the direction of
  decreasing electric potential.
• Potential due to a set of charges
• Properties of Conductors
• All points on the conductor (surface bulk ) are
  at the same potential
• Charge concentrates on pointy surfaces.

3
Example

• A spherical drop of water carrying a charge of
  30pC has a potential of 500V at its surface (with
  V0 at infinity).
• What is the radius of the drop?
• If two such drops of the same charge and radius
  combine to form a single drop, what is the
  potential at the surface of the new drop?

4
E-fields from V

• Potential
• OR

5
Example E from V

• Compute the Electric field in a region where the
  potential is

6
Equipotential surfaces

• Equipotentials connect points of the same
  potential.
• Similar to contour lines on a topographical map,
  which connect points of the same elevation, and
  to isotherms (lines of constant temperature) on a
  weather map.

• No net work is done by the E-field when a charge
  moves from one point to another on the
  equipotential surface.

7
Equipotential Surfaces

• point charge family of concentric spheres.
• Uniform electric field family of planes
  perpendicular to the field
• What are equipotentials good for?
• make it easy to determine how much work is needed
  to move a charge from one place to another.
• It takes no work to move a charge along an
  equipotential.
• As E is perpendicular to the displacement

8
Equipotential Surfaces

• point charge family of concentric spheres.
• Uniform electric field family of planes
  perpendicular to the field
• What are equipotentials good for?
• make it easy to determine how much work is needed
  to move a charge from one place to another.
• It takes no work to move a charge along an
  equipotential.
• The more equipotential lines are crossed, the
  more work is associated with the trip.

9
Equipotentials

1. Which direction is the E-field?
2. In which case is the E-field strongest?
3. If a particle with charge q moves from a to b,
   in which situation does it experiences the
   largest change in potential energy?

Case 2
Case 2
Case 1 V 10 4 -6
Case 2 V 20 8 -12
b
a
10
Lightning Storms
E fields
Equipotential Surfaces
Moro Rock in California's Sequoia National Park
11
Equipotentials

• Three points A, B, and C are shown in the
  vicinity of a positive point charge. Which takes
  more work, moving a negative charge from A to C,
  OR from B to C.
• Moving from A to C takes more work
• Moving from B to C takes more work
• Neither, the work required is the same for both
  cases.

12
Example Equipotential Surfaces

• A metal sphere carries a charge Q0.50 C. Its
  surface is at a potential of 15000 V.
  Equipotential surfaces are to be drawn for 100V
  intervals outside the sphere.
• Determine the radius for 1st, 10th and 100th
  equipotential from the surface.

13
Quiz Time?
14
Quiz Solution

• Two charged conducting spheres of different radii
  are connected by a conducting wire.
• X The sphere with the smaller radius has
  higher surface charge density.
• Comparing points A, B, C, and D only, at which of
  those points is the magnitude of the electric
  field largest?
• A X B C D
• all four points would be on the same field
  line,
• so the magnitude of the field would be
  equal at those points
• If you draw field lines youll see that they are
  closest together at B, at least for those 4
  points.
• Comparing points B and E only, at which point is
  the magnitude
• of the electric field largest?
• B X E both points are on
  the same equipotential,
• so the magnitude of the field would be
  equal at both points
• The magnitude of the field is proportional to how
  quickly
• the potential changes with distance. E dV/dr,
  and to
• achieve the same dV from point E requires a
  smaller
• distance, so E is larger at point E.
• sketch the electric field line passing through
  point E.

15
Chapter 24 Capacitance

• Capacitors (or condensors)
• Device for storing charge/energy
• Camera flashes, circuit applications (radio
  tuners), computer key boards.
• Capacitance C
• the amount of charge a capacitor can store for a
  given potential difference
• For a capacitor with a charge of Q on one plate
  and -Q on the other Q C ?V (C gt 0)
• Unit of Capacitance is Farad (F) (1F
  1C/1V)
• For a parallel-plate capacitor
• The energy stored in a capacitor is

16
Playing with a Capacitor

• Take a parallel-plate capacitor and connect it to
  a power supply. The power supply sets the
  potential difference between the plates of the
  capacitor.
• The distance between the capacitor plates can be
  changed. While the capacitor is still connected
  to the power supply, the distance between the
  plates is increased. When this occurs, what
  happens to C, Q, and ?V?
• C decreases, Q decreases, and ?V stays the
  same
• C decreases, Q increases, and ?V increases
• C decreases, Q stays the same, and ?V
  increases
• All three decrease
• None of the above

Q C ?V
17
Playing with a Capacitor

• Take a parallel-plate capacitor and connect it to
  a power supply. The power supply sets the
  potential difference between the plates of the
  capacitor.
• Now the capacitor is charged by the power supply
  and then the connections to the power supply are
  removed. When the distance
• between the plates is increased now, what happens
  to Q, C, and ? V?
• C decreases, Q decreases, and ?V stays the
  same
• C decreases, Q increases, and ?V increases
• C decreases, Q stays the same, and ?V
  increases
• All three decrease
• None of the above

Q C ?V
18
Capacitance

• Will the changes below cause the capacitance of
  a parallel-plate capacitor to increase, decrease,
  or stay the same.
• Increase the area of each plate
• ? C INCREASES
• Double the charge on each plate
• ? C stays the same
• Increase the potential difference across the
  capacitor ? C stays the same
• Increase the distance between the plates
• ? C DECREASES

19
Multiple Capacitors in circuits

• Devices in parallel same potential difference
  across them.
• Charge on the equivalent capacitor sum of the
  charges on each capacitor.
• Devices in series all of them have the same
  charge.
• Total potential difference across the chain sum
  of the potential differences across each one of
  them.

Ceq C1 C2 ...
20

• Read, Read, Read .
• Chapter 25