Lecture 6
Chapter 25
The Electric Potential
Course website: http://faculty.uml.edu/Andriy_Danylov/Teaching/PhysicsII
PHYS.1440 Lecture 6 Danylov Department of Physics and Applied Physics Today we are going to discuss:
Chapter 25:
Section 25.4-7 Electric Potential
PHYS.1440 Lecture 6 Danylov Department of Physics and Applied Physics The electric potential q Consider a charge Q which creates an electric field U V Q Quantities Vectors Scalars describing: 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 PHYS.1440 Lecture 6 Danylov Department of Physics and Applied Physics Once the potential has been determined, it’s easy to find the potential energy
V(r)
It is similar to
PHYS.1440 Lecture 6 Danylov 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 The electric potential E V Es (definition) q So V Es where s is the distance from the negative electrode The electric potential inside a parallel-plate capacitor
s 0 s d s
The potential difference VC, or “voltage” between the two capacitor plates is
V C V V Ed 0 Ed
PHYS.1440 Lecture 6 Danylov Department of Physics and Applied Physics Equipotential surfaces V Es E
s 0 s d s Equipotential surfaces An equipotential surface/line is one on which all points are at the same potential
The electric field vectors are perpendicular to the equipotential surfaces
PHYS.1440 Lecture 6 Danylov Department of Physics and Applied Physics 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 It’s a scalar 4 This expression for V assumes that we have chosen V = 0 to be at r = .
The potential extends through all of space, showing Equipotential lines the influence of charge Q, but it weakens with distance as 1/r.
PHYS.1440 Lecture 6 Danylov Department of Physics and Applied Physics ConcepTest Equipotential of Point Charge A) A and C Which two points have B) B and E the same potential? C) B and D D) C and E E) no pair
Since the potential of a point charge is: A Q V k r C only points that are at the same distance Q from charge Q are at the same potential. B E D This is true for points C and E. They lie on an equipotential surface.
Follow-up: Which point has the smallest potential? Equipotential surfaces
PHYS.1440 Lecture 6 Danylov Department of Physics and Applied Physics The principle of superposition
If there are many charges. The electric potential, like the electric field, obeys the principle of superposition.
Q1 r1 P
r2 -Q2 1 1 1 r r 3 4 4 4
Q3
You see. The principle of superposition is so much easier with scalars
PHYS.1440 Lecture 6 Danylov Department of Physics and Applied Physics ConcepTest Equipotential of Point Charge At the midpoint between A) E 0; V = 0 these two equal but B) E 0; V > 0 opposite charges, C) E 0; V < 0 D) E points right; V = 0 E) E points left; V = 0
The principle of superposition
+ 0 ConcepTest Electric Potential
What is the electric A) V > 0 potential at point A? B) V = 0 C) V < 0 1 4
A B + 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. ConcepTest Equipotential Surfaces A At which point E) all of them does V = 0? B
C +Q –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 Hollywood Square Four point charges are A) E = 0 V = 0 arranged at the corners of a B) E = 0 V 0 square. Find the electric C) E 0 V 0 field E and the potential V at D) E 0 V =0 the center of the square. E) E = V regardless of the value
The potential is zero: the scalar -Q contributions from the two positive +Q 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). -Q +Q Follow-up: What is the direction of the electric field at the center? The electric potential of a continuous distribution of charge
PHYS.1440 Lecture 6 Danylov Department of Physics and Applied Physics Example
PHYS.1440 Lecture 6 Danylov 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
PHYS.1440 Lecture 6 Danylov Department of Physics and Applied Physics Thank you See you next time
PHYS.1440 Lecture 6 Danylov Department of Physics and Applied Physics