l8 ch25 el potential · 2020. 2. 13. · phys.1440 lecture 8a.danylov department of physics and...

PHYS.1440 Lecture 8 A.DanylovDepartment of Physics and Applied Physics

Lecture 8

Chapter 25

The Electric Potential

Physics II

Cool! Scalar quantities are so much better

Course website:https://sites.uml.edu/andriy-danylov/teaching/physics-ii/


Today we are going to discuss:

Chapter 25:

Section 25.4-7 Electric Potential


Quantities describing:

Vectors Scalars

Interactions between charges

Field

The electric potential

𝑭𝒌𝒒𝑸𝒓𝟐 𝒓

𝑼 𝒓𝒌𝒒𝑸𝒓

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

(Electric field)


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

V(r)

It is similar to

E

𝑽 𝒓𝑼 𝒓𝒒

q


The Electric Potential Inside a Parallel-Plate Capacitor

E

sds 0s

q

qEsU Thepotentialenergyofqinauniformelectricfield

𝑉 𝑟𝑈 𝑟𝑞

Theelectricpotential(definition)

So EsV

Theelectricpotentialinsideaparallel‐platecapacitorwhere sis the distance from the negativeelectrode

The potentialdifferenceVC, or “voltage” between the two capacitor plates is

Δ𝑉 𝑉 𝑉 𝐸𝑑 0 𝐸𝑑

EsV

Δ𝑉 𝐸𝑑


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


The Electric Potential of a Point Charge

q𝑈 𝑟 𝑘

𝑞𝑄𝑟

We derived the potential energy of two point charges

r

𝑉 𝑟𝑈 𝑟𝑞

The electric potential due to a point charge Q is

𝑉 𝑘𝑄𝑟

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 distance from charge Q are at the same potential. This is true for points C and E.

They lie on an equipotentialsurface.

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 Q

𝑉 𝑘𝑄𝑟

Follow-up: Which point(s) has the smallest potential?

ConcepTest Equipotential of Point Charge


Equipotential surfaces(examples)


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.

𝑉 𝑟 𝑉 𝑉 𝑉

𝑘𝑄𝑟

𝑘𝑄𝑟 𝑘

𝑄𝑟

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

𝑉 𝑘𝑄𝑟

I am falling in love with scalar quantities

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,

𝐸

𝐸𝑉 𝑉 𝑉

The principle of superposition

𝑘 + 𝑘 0

ConcepTest Equipotential of Point Charge


The electric potential of a continuous distribution of charge

Integration again!!!


Example

It is trivial!

End of class

Four point charges are arranged at thecorners of a square. Find the electricfield E and the potential V at the centerof 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

A

C

B

D

+Q –Q

E)allofthem

All of the points are equidistant from both charges. Since the charges are equal and opposite, their contributions to the potential cancel outeverywhere along the mid-plane between the charges.

Follow-up: What is the direction of the electric field at all 4 points?

ConcepTest Equipotential Surfaces

At which point does V = 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) V >0

B) V =0

C) V <0

A B

What is the electric potential at point A?

𝑉 𝑘𝑄𝑟

𝑉 𝑉 𝑉

𝑘 + k 0 𝑠𝑖𝑛𝑐𝑒 𝑟 𝑟

ConcepTest Electric Potential


Potentialofachargedrod

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

Example


Thank you

l8 ch25 el potential · 2020. 2. 13. · phys.1440 lecture 8a.danylov department of physics and...

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