the electric potential energy -...

Department of Physics and Applied PhysicsPHYS.1440 Lecture 5 Danylov

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

Lecture 5

Chapter 25

The Electric Potential Energy


Today we are going to discuss:

Chapter 25:

Section 25.1 Electric Potential Energy Section 25.2 The potential energy of a point charge


Idea!!!!

New Idea

Let’s introduce scalar quantities instead of a FORCE and FIELD

So far, we used vector quantities: 1. Electric Force (F)

2. Electric Field (E)

But, as you know, it is not easy to deal with vectors

Depressed!


PE idea: That is what we have in our example. So, you can “attach” this number to the final point and give this number 5 a fancy name – the potential energy (PE) (Uf=5J) with respect to the initial point, where we can assume PE to be zero (the reference point). For every conservative force a potential energy can be introduced.

Since the gravitational and electrical forces are conservative forces, corresponding potential energies can be introduced.

Uf=5J

F

i

f

If a work done by a force is path independent, then thisforce is called conservative (since it leads to conservationof mechanical energy)

ds Recall for Physics I, a work done by a force

∙

U0

Consider different paths between two points in a field

Let’s define a conservative force and give an idea of PE


Since the gravitational force is a conservative force, agravitational potential energy (scalar quantity) can beintroduced.

Ugrav mgy

U0 =0 (Reference Level)

Uinitial U0 + mgyi

Ufinal U0 + mgyf

Gravitation

F=mg

i

f

This fall can be described using a gravitational force(vector quantity), which describes an interaction betweenthe Earth and a cat.

Fgrav mg

G

Electrostatics

F=qE

i

f

Let’s derive these electric PE:

UniformElectric field

k

The case of two point charges

U rkr

Fel qE U qEs

G

Goal 1

Goal 2The case of two point massesPhysics I


Potential energy is an energy of interaction,

so there must be at least two interacting electric objects.


Potential energy of q in a uniform electric field

(in a capacitor)


Potential energy of q in a uniform electric field

f

i

sdFW

WU K

f

i

sdEq

E

s0 isfs

q

sd

f

i

Edsq f

i

dsqE

E

if ssqE

Recall from Physics I

if UUU if ssqE

qEsUU 0

ifif qEsqEsUU To get the most general expression, let’s introduce U0,

which is a potential energy at the reference point s=0

if qEsUUqEs 00if UU

The work done on q is:

Electric potential energy of charge q and a charged capacitor

F

↑↓

Consider a positive charge q inside a capacitor. It speeds up as it “falls” toward the negative plate.

There is a constant force F qE towards the negative plate

It is convenient to choose the potential energy at the reference point 00 U qEsU


Potential energy of a positive charge, +q

s0WU K

0K

0UIf we use Conservation of energy

plateplate KK

plateplate UU )()( platenearplatenear ss

We will get

If +q moves in the direction of E, then

higher PElower PE

Ok, now we know the PE expression of a charge inside of a capacitor. Let’s play with that expression to see where PE is larger or smaller, etc.

qEsU


Potential energy of a positive charge, -q

WU K0K

0UIf we use conservation of energy

plateplate KK

plateplate UU )()( platenearplatenear ss

We will get

If -q moves in the direction opposite of E, then

s0

EsqU higher PE(less negative)

lower PE(more negative)

From these two examples, you see that PE can be used to analyze motion instead of force.

Since, the charge is negative, let’s rewrite U in this form

ConcepTest Potential energyA) Charge A

B) Charge B

C) They have the same potential energy

D) Both have zero potential energy

Two positive charges are equal. Which has more electric potential energy?

qEsU

s

A) Charge A

B) Charge B

C) They have the same potential energy

D) Both have zero potential energy

Two negative charges are equal. Which has more electric potential energy?

s

EsqU

ConcepTest Potential energy

A) Increases.

B) Remains constant.

C) Decreases.

A positive charge moves as shown. Its kinetic energy

increases

decreases

sqEsU

U K

0U

0K



Potential energy of two point charges


The potential energy of two point charges

This is explicitly the energy of the system, not the energy of just q or Q.

Note that the potential energy of two charged particles approaches zero as r .

A) A positive potential energy becomes more positive.

B) A positive potential energy becomes less positive.

C) A negative potential energy becomes more negative.

D) A negative potential energy becomes less negative.E) A positive potential energy becomes a negative potential energy.

A positive and a negative charge are released from rest in vacuum. They move toward each other. As they do:



Example 25.2

Example Approaching a charged sphere


Thank youSee you next time

the electric potential energy -...

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