Announcements• Homework:

– Webassign HW due on SUNDAY at 11:59pm– No Hand-in Homework

• Test 1:– Feb 17th, 6-7:30 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)

Summary: Electric Potential• Electric Potential

– Reference point: V=0 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.

Example

• A spherical drop of water carrying a charge of 30pC has a potential of 500V at its surface (with V=0 at infinity).

1. What is the radius of the drop?

2. 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?

E-fields from V

• Potential:

• OR

Example: E from V

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

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.

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

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.

Equipotentials1. 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 1V

10

4

-6

Case 2 V

20

8

-12

Case 2

a

b

Case 2

Lightning Storms

E fields

Equipotential Surfaces

Moro Rock in California's Sequoia National Park

B AC

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.

1. Moving from A to C takes more work

2. Moving from B to C takes more work

3. Neither, the work required is the same for both cases.

Example: Equipotential Surfaces

• A metal sphere carries a charge Q=0.50 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.

Quiz Time?

Quiz SolutionTwo 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 you’ll 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.– field lines are perpendicular to equipotentials, and that the direction of the field is in the direction of decreasing potential.

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 > 0)– Unit of Capacitance is Farad (F) (1F = 1C/1V)

• For a parallel-plate capacitor • The energy stored in a capacitor is

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?

1. C decreases, Q decreases, and V stays the same 2. C decreases, Q increases, and V increases 3. C decreases, Q stays the same, and V increases 4. All three decrease 5. None of the above

Q = C V

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?

1. C decreases, Q decreases, and V stays the same 2. C decreases, Q increases, and V increases 3. C decreases, Q stays the same, and V increases 4. All three decrease 5. None of the above

Q = C V

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

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 + ...

• Read, Read, Read ….

Chapter 25