1. Physics 2102 Lecture: 10 WED 04 FEB
Jonathan Dowling
Physics Lecture: 10 WED 04 FEB
Electric Potential III
Ch24.11–12

2. PHYS2102 FIRST MIDTERM EXAM!
6–7PM THU 05 FEB 2009
Dowling’s Sec. 2 in Lockett Hall, Room 6
YOU MUST BRING YOUR STUDENT ID!
YOU MUST WRITE UNITS TO GET FULL CREDIT!
The exam will cover chapters 21 through 24, as covered in homework sets 1, 2, and 3. The formula sheet for the exam can be found here:
KNOW SI PREFIXES n, cm, k, etc.
THERE WILL BE A REVIEW SESSION 6–7PM WED 04 FEB 2009 in Williams 103

3. Continuous Charge Distributions
Divide the charge distribution into differential elements
Write down an expression for potential from a typical element — treat as point charge
Integrate!
Simple example: circular rod of radius r, total charge Q; find V at center. r dq

4. Potential of Continuous Charge Distribution: Line of Charge
Uniformly charged rod
Total charge Q
Length L
What is V at position P? x P dx L a
Units: [Nm2/C2][C/m]=[Nm/C]=[J/C]=[V]

5. Electric Field & Potential: A Simple Relationship!
Focus only on a simple case: electric field that points along +x axis but whose magnitude varies with x.
Notice the following:
Point charge:
E = kQ/r2
V = kQ/r
Dipole (far away):
E = kp/r3
V = kp/r2
E is given by a DERIVATIVE of V!
Of course!
Note:
MINUS sign!
Units for E: VOLTS/METER (V/m)

6. E from V: Example Uniformly charged rod Total charge Q Length L
We Found V at P!
Find E from V? x P dx L a
Units:
√ Electric Field!

7. Electric Field & Potential: Question
Hollow metal sphere of radius R has a charge +q
Which of the following is the electric potential V as a function of distance r from center of sphere? +q V r
r=R
(b) V r
r=R
(a) V r
r=R
(c)

8. Electric Field & Potential: Example
Outside the sphere:
Replace by point charge!
Inside the sphere:
E = 0 (Gauss’ Law)
E = –dV/dr = 0 IFF V=constant +q E V

9. Equipotentials and Conductors
Conducting surfaces are EQUIPOTENTIALs
At surface of conductor, E is normal (perpendicular) to surface
Hence, no work needed to move a charge from one point on a conductor surface to another
Equipotentials are normal to E, so they follow the shape of the conductor near the surface. V E

10. Conductors Change the Field Around Them!
An Uncharged Conductor:
A Uniform Electric Field:
An Uncharged Conductor in the Initially Uniform Electric Field:

11. Sharp Conductors
Charge density is higher at conductor surfaces that have small radius of curvature
E = s/e0 for a conductor, hence STRONGER electric fields at sharply curved surfaces!
Used for attracting or getting rid of charge:
lightning rods
Van de Graaf -- metal brush transfers charge from rubber belt
Mars pathfinder mission -- tungsten points used to get rid of accumulated charge on rover (electric breakdown on Mars occurs at ~100 V/m)
(NASA)

12. Ben Franklin Invents the Lightning Rod!

13. Summary:
Electric potential: work needed to bring +1C from infinity; units = V = Volt
Electric potential uniquely defined for every point in space -- independent of path!
Electric potential is a scalar -- add contributions from individual point charges
We calculated the electric potential produced by a single charge: V = kq/r, and by continuous charge distributions :
V = kdq/r
Electric field and electric potential: E= -dV/dx
Electric potential energy: work used to build the system, charge by charge. Use W = U = qV for each charge.
Conductors: the charges move to make their surface equipotentials.
Charge density and electric field are higher on sharp points of conductors.