Lecture 7 Chapter 28
Physics II 02.09.2015
The Electric Potential 95.144 Course website: http://faculty.uml.edu/Andriy_Danylov/Teaching/PhysicsII Lecture Capture: http://echo360.uml.edu/danylov201415/physics2spring.html
95.144, Spring 2015, Lecture 7
Department of Physics and Applied Physics
The electric potential q Consider a charge Q which creates an electric field
V
Q Quantities describing:
Vectors
U
Scalars If F is conservative
Interactions between charges (Force - vector)
(potential energy - scalar)
Field (Electric field)
(Electric potential)
Similar to the way we introduced the electric field instead of a force (to remove q), we can introduce the ELECTRIC POTENTIAL instead of the potential energy The unit 95.144, Spring 2015, Lecture 7
Department of Physics and Applied Physics
Once the potential has been determined, it’s easy to find the potential energy
V(r)
95.144, Spring 2015, Lecture 7
Department of Physics and Applied Physics
The Electric Potential Inside a Parallel-Plate Capacitor The potential energy of q in a uniform electric field
U qEs
E
The electric potential (definition)
V Es q
So
V Es
where s is the distance from the negative electrode The electric potential inside a parallel-plate capacitor
s 0
sd
s
The potential difference VC, or “voltage” between the two capacitor plates is
VC V V
Ed 0 Ed
95.144, Spring 2015, Lecture 7
Department of Physics and Applied Physics
Equipotential surfaces An equipotential surface/line is one on which all points are at the same potential
V Es
E
s 0
sd
Equipotential surfaces The electric field vectors are perpendicular to the equipotential surfaces 95.144, Spring 2015, Lecture 7
Department of Physics and Applied Physics
s
The Electric Potential of a Point Charge We derived the potential energy of the two point charges
q
1
r
4
Q The electric potential due to a point charge q is
1 4
It’s a scalar
This expression for V assumes that we have chosen V = 0 to be at r = .
Equipotential lines
The potential extends through all of space, showing the influence of charge Q, but it weakens with distance as 1/r.
95.144, Spring 2015, Lecture 7
Department of Physics and Applied Physics
ConcepTest 1 Equipotential of Point Charge A) A and C Which two points have the same potential?
B) B and E C) B and D D) C and E E) no pair
Since the potential of a point charge is:
A
Q V k r only points that are at the same distance from charge Q are at the same potential. This is true for points C and E.
C B
They lie on an equipotential surface. Follow-up: Which point has the smallest potential?
E
Q
D
Equipotential surfaces
95.144, Spring 2015, Lecture 7
Department of Physics and Applied Physics
The principle of superposition If there are many charges.
r1
Q1
The electric potential, like the electric field, obeys the principle of superposition.
P
r2
- Q2
1
r3
r
4
1 4
1 4
Q3 You see. The principle of superposition is so much easier with scalars 95.144, Spring 2015, Lecture 7
Department of Physics and Applied Physics
Channel 61
ConcepTest 2 Electric Potential
At the midpoint between these two equal but opposite charges,
A) E 0; V = 0 B) E 0; V > 0 C) E 0; V < 0 D) E points right; V = 0 E) E points left; V = 0 The principle of superposition
+
0
ConcepTest 3 Electric Potential I 1) V > 0
What is the electric potential at point A?
2) V = 0 3) V < 0
1 4
+
0
Since Q2 (which is positive) is closer to point A than Q1 (which is negative) and since the total potential is equal to V1 + V2, the total potential is positive.
A
B
ConcepTest 4 Equipotential Surfaces I A E) all of them
At which point does V = 0?
B
+Q
C
–Q
D All of the points are equidistant from both charges. Since the charges are equal and opposite, their contributions to the potential cancel out everywhere along the mid-plane between the charges. Follow-up: What is the direction of the electric field at all 4 points?
ConcepTest 5 Hollywood Square Four point charges are arranged at the corners of a square. Find the electric field E and the potential V at the center of the square.
1) E = 0
V=0
2) E = 0
V0
3) E 0
V0
4) E 0
V=0
5) E = V regardless of the value The potential is zero: the scalar contributions from the two positive charges cancel the two minus charges. However, the contributions from the electric field add up as vectors, and they do not cancel (so it is non-zero). Follow-up: What is the direction of the electric field at the center?
-Q
+Q
-Q
+Q
The electric potential of a continuous distribution of charge
95.144, Spring 2015, Lecture 7
Department of Physics and Applied Physics
95.144, Spring 2015, Lecture 7
Department of Physics and Applied Physics
Potential of a charged rod Determine the potential V(x) for points along the x axis outside the charged rod of length 2l. The total charge is Q. Let V=0 at infinity
95.144, Spring 2015, Lecture 7
Department of Physics and Applied Physics
What you should read Chapter 28 (Knight) Sections
28.4 28.5 28.6 28.7
95.144, Spring 2015, Lecture 7
Department of Physics and Applied Physics
Thank you See you on Friday
95.144, Spring 2015, Lecture 7
Department of Physics and Applied Physics
