Department of Physics and Applied PhysicsPHYS.1440 Lecture 6 Danylov

Course website:http://faculty.uml.edu/Andriy_Danylov/Teaching/PhysicsII

Lecture 6

Chapter 25

The Electric Potential

Department of Physics and Applied PhysicsPHYS.1440 Lecture 6 Danylov

Today we are going to discuss:

Chapter 25:

Section 25.4-7 Electric Potential

Department of Physics and Applied PhysicsPHYS.1440 Lecture 6 Danylov

Quantities describing:

Vectors Scalars

Interactions between charges

Field

The electric potentialConsider a charge Q which creates an electric field

Q

qU

If F is conservative

(Force - vector) (potential energy - scalar)

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

(Electric potential)

The unit

V

(Electric field)

Department of Physics and Applied PhysicsPHYS.1440 Lecture 6 Danylov

Once the potential has been determined, it’s easy to find the potential energy

V(r)

It is similar to   

Department of Physics and Applied PhysicsPHYS.1440 Lecture 6 Danylov

The Electric Potential Inside a Parallel-Plate Capacitor

E

sds 0s

q

qEsU The potential energy of q in a uniform electric field

The electric potential(definition)

So EsV

The electric potential inside a parallel-plate capacitor

where s is the distance from the negative electrode

The potential difference VC, or “voltage” between the two capacitor plates is

VVV C EdEd 0

EsV

Department of Physics and Applied PhysicsPHYS.1440 Lecture 6 Danylov

Equipotential surfaces

E

sds 0sEquipotential surfaces

EsV

The electric field vectors are perpendicular to the equipotential surfaces

An equipotential surface/line is one on which all points are at the same potential

Department of Physics and Applied PhysicsPHYS.1440 Lecture 6 Danylov

The Electric Potential of a Point Charge

q 14

We derived the potential energy of the two point charges

r

The electric potential due to a point charge Q is

14

This expression for V assumes that we have chosen V = 0 to be at r = .

The potential extends through all of space, showing the influence of charge Q, but it weakens with distance as 1/r.

It’s a scalar

Equipotential lines

Q

Since the potential of a point charge is:

only points that are at the same distancefrom charge Q are at the same potential. This is true for points C and E.

They lie on an equipotential surface.

Which two points have the same potential?

A) A and C

B) B and E

C) B and D

D) C and E

E) no pair

A

C

B DE QrQkV

Follow-up: Which point has the smallest potential?

ConcepTest Equipotential of Point Charge

Department of Physics and Applied PhysicsPHYS.1440 Lecture 6 Danylov

Equipotential surfaces

Department of Physics and Applied PhysicsPHYS.1440 Lecture 6 Danylov

The principle of superposition

Q1

- Q2

r1

Q3

Pr2

r3

The electric potential, like the electric field, obeys the principle of superposition.

If there are many charges.

1

4r1

41

4

You see. The principle of superposition is so much easier with scalars

A) E 0; V = 0

B) E 0; V > 0

C) E 0; V < 0

D) E points right; V = 0E) E points left; V = 0

At the midpoint between these two equal but opposite charges,

The principle of superposition

+  0

ConcepTest Equipotential of Point Charge

Since Q2 (which is positive) is closerto point A than Q1 (which is negative) and since the total potential is equal to V1 + V2, the total potential is positive.

A) V > 0

B) V = 0

C) V < 0

A B

What is the electric potential at point A?

14

+  0

ConcepTest Electric Potential

At which point does V = 0?

A

C

B

D

+Q –Q

E) all of them

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 Equipotential Surfaces

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.

A) E = 0 V = 0

B) E = 0 V 0

C) E 0 V 0

D) E 0 V = 0

E) E = V regardless of the value

-Q

-Q +Q

+Q

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?

ConcepTest Hollywood Square

Department of Physics and Applied PhysicsPHYS.1440 Lecture 6 Danylov

The electric potential of a continuous distribution of charge

Department of Physics and Applied PhysicsPHYS.1440 Lecture 6 Danylov

Example

Department of Physics and Applied PhysicsPHYS.1440 Lecture 6 Danylov

Potential of a charged rod

Determine the potential V(x) for points along the x axis outside the charged rodof length 2l. The total charge is Q. Let V=0 at infinity

Department of Physics and Applied PhysicsPHYS.1440 Lecture 6 Danylov

Thank youSee you next time