# Briefly review the concepts of potential energy and work. · 2012. 8. 21. · Potential Energy...

of 17
/17

Embed Size (px)

### Transcript of Briefly review the concepts of potential energy and work. · 2012. 8. 21. · Potential Energy...

Microsoft PowerPoint - chapter23•Potential Energy = U = stored work
in a system

•Work = energy put into or taken out of system by forces

•Work done by a (constant) force F :

θcos|||| rFrFW v

r

F

θ

Gravitational Potential Energy Lift a book by hand (Fext) at constant velocity.

F ext

Note that get to define U=0,

typically at the ground.

“internal energy” in Thermo.

Gravitational Potential Energy (cont)

is conserved.

Coulomb force is also a conservative force.

Friction is not a conservative force.

If only conservative forces are acting, then

E Mech

- - - - - - - - - - - - - -

+

Initial position

Final position

Uelec = change in U when moving +q from initial to final position.

fieldextif WWUUU −=+=−=

rEqU v

from initial (i) position to final (f)

position.

Electric Potential Energy Since Coulomb forces are conservative, it means that the change

in potential energy is path independent.

∫ ⋅−= f

i

Electric Potential Energy Positive charge in a constant field

Electric Potential Energy Negative charge in a constant field

Observations • If we need to exert a force to “push” or “pull” against the

field to move the particle to the new position, then U

increases. In other words “we want to move the particle to

the new position” and “the field resists”.

• If we need to exert a force to “hold” the particle so the field

will not move the particle to the new position, then U

decreases. In other words, “the field wants to move the

particle”, and “we resist”.

• Both can be summarized in the following statement:

“If the force exerted by the field opposes the motion of the

particle, the field does negative work and U increases,

otherwise, U decreases”

charges

2

Imagine doing work to move the objects from infinitely far apart

(initial) to the configuration drawn above (final).

11

constant over the path!

from infinity to r.

r+Q 1 +Q

Moving Q 2

through the field.

Potential Energy between two point charges

We also need to define the zero point for potential energy.

This is arbitrary, but the convention is U=0 when all charged

objects are infinitely far apart.

r

Potential Energy between two

E. Potential energy vs. distance

E. Potential Energy of a charge

distribution

an integral

r1 r2

distribution

an integral

energy we have to consider all the

fields produced by all the charges qi

on the other(n-1) charges qj

r1 r2

point charges separated by a

distance r.

negative charges? A) Left Plot,

B) Right Plot

energy.

Earlier we found that not only using forces, but also electric fields

was very useful.

2

•Electric Field is the force per unit of charge due to the presence of Q 1

•Electric field from Q 1

is there even if Q 2

is not there.

Electric Field

We find a similarly useful thing with electric potential energy.

r

2

•Electric potential is the electric potential energy per unit of charge due

to the presence of Q 1

•Electric potential from Q 1

is there even if Q 2

is not there.

Electric Potential

+Q 1

a source charge Q 1 .

Units are [Newtons/Coulomb].

a source charge Q 1 .

Units are [Joules/Coulomb] or [Volts].

r r

Electric Potential of a point charge

r

Analogy: Electrical pressure or electrical "height"

Positive charges want to get away from higher voltage towards lower voltage.

Just like a gas wants to move from high to low pressure.

Electric Potential of a charge

distribution

an integral

field produced by the charges qi

Electric potential due to charges qi

∑= i i

∫∫ ⋅−=⋅−== f

i

f

i

constant elevation.

Gravitational potential

elevation I have a

scalar.

constant Voltage (equipotentials).

Voltage, it has an electrical

potential energy [Joules] = qV

•Equi-potential surfaces and field lines are always mutually

perpendicular

and larger values of |E|

E. Field and E. potential

What is Electric Field?

analogous to a steepness

depends which direction you

as a function of position, we can

compute Voltage.

find the change in elevation.

This does not depend on our path taken.

E. Field and E. potential

V i =V(∞)= 0 by our convention.

dz

of Voltage in a given direction. z

z

VE ∇−= rv The Electric field vector “potential gradient”

http://www.falstad.com/vector2de/

30

CPS question

Two identical charge, +Q and +Q, are fixed in space. The electric potential (V) at the point X midway between the charges is: A) Zero B) Non-Zero

+Q +Q Point X

CPS Question

Drawn are a set of equipotential lines. Consider the electric field at points A and B. Which of the following statements is true?

0V 10V 20V 30VPoint A

Point B

A) |EA| > |EB| B) |EA| < |EB| C)|EA| = |EB| D)Not enough information given. E) None of the above

32

CPS Question

Two charges, +Q and -Q, are fixed in space. The electric field at the point X midway between the charges is: A) Zero B) Non-Zero

+Q -Q Point X

Point P

The magnitude of the electric field at point P is: A) Zero B) Non-Zero

The magnitude of the voltage at point P is: A) Zero B) Non-Zero

All points on conductor must be at the same

electrical potential.

Imagine point a at Voltage V a .

Since E=0 everywhere inside the conductor (no steepness), integral to

point b is always 0. V ab =0.

E. Potential inside conductors

•Work = energy put into or taken out of system by forces

•Work done by a (constant) force F :

θcos|||| rFrFW v

r

F

θ

Gravitational Potential Energy Lift a book by hand (Fext) at constant velocity.

F ext

Note that get to define U=0,

typically at the ground.

“internal energy” in Thermo.

Gravitational Potential Energy (cont)

is conserved.

Coulomb force is also a conservative force.

Friction is not a conservative force.

If only conservative forces are acting, then

E Mech

- - - - - - - - - - - - - -

+

Initial position

Final position

Uelec = change in U when moving +q from initial to final position.

fieldextif WWUUU −=+=−=

rEqU v

from initial (i) position to final (f)

position.

Electric Potential Energy Since Coulomb forces are conservative, it means that the change

in potential energy is path independent.

∫ ⋅−= f

i

Electric Potential Energy Positive charge in a constant field

Electric Potential Energy Negative charge in a constant field

Observations • If we need to exert a force to “push” or “pull” against the

field to move the particle to the new position, then U

increases. In other words “we want to move the particle to

the new position” and “the field resists”.

• If we need to exert a force to “hold” the particle so the field

will not move the particle to the new position, then U

decreases. In other words, “the field wants to move the

particle”, and “we resist”.

• Both can be summarized in the following statement:

“If the force exerted by the field opposes the motion of the

particle, the field does negative work and U increases,

otherwise, U decreases”

charges

2

Imagine doing work to move the objects from infinitely far apart

(initial) to the configuration drawn above (final).

11

constant over the path!

from infinity to r.

r+Q 1 +Q

Moving Q 2

through the field.

Potential Energy between two point charges

We also need to define the zero point for potential energy.

This is arbitrary, but the convention is U=0 when all charged

objects are infinitely far apart.

r

Potential Energy between two

E. Potential energy vs. distance

E. Potential Energy of a charge

distribution

an integral

r1 r2

distribution

an integral

energy we have to consider all the

fields produced by all the charges qi

on the other(n-1) charges qj

r1 r2

point charges separated by a

distance r.

negative charges? A) Left Plot,

B) Right Plot

energy.

Earlier we found that not only using forces, but also electric fields

was very useful.

2

•Electric Field is the force per unit of charge due to the presence of Q 1

•Electric field from Q 1

is there even if Q 2

is not there.

Electric Field

We find a similarly useful thing with electric potential energy.

r

2

•Electric potential is the electric potential energy per unit of charge due

to the presence of Q 1

•Electric potential from Q 1

is there even if Q 2

is not there.

Electric Potential

+Q 1

a source charge Q 1 .

Units are [Newtons/Coulomb].

a source charge Q 1 .

Units are [Joules/Coulomb] or [Volts].

r r

Electric Potential of a point charge

r

Analogy: Electrical pressure or electrical "height"

Positive charges want to get away from higher voltage towards lower voltage.

Just like a gas wants to move from high to low pressure.

Electric Potential of a charge

distribution

an integral

field produced by the charges qi

Electric potential due to charges qi

∑= i i

∫∫ ⋅−=⋅−== f

i

f

i

constant elevation.

Gravitational potential

elevation I have a

scalar.

constant Voltage (equipotentials).

Voltage, it has an electrical

potential energy [Joules] = qV

•Equi-potential surfaces and field lines are always mutually

perpendicular

and larger values of |E|

E. Field and E. potential

What is Electric Field?

analogous to a steepness

depends which direction you

as a function of position, we can

compute Voltage.

find the change in elevation.

This does not depend on our path taken.

E. Field and E. potential

V i =V(∞)= 0 by our convention.

dz

of Voltage in a given direction. z

z

VE ∇−= rv The Electric field vector “potential gradient”

http://www.falstad.com/vector2de/

30

CPS question

Two identical charge, +Q and +Q, are fixed in space. The electric potential (V) at the point X midway between the charges is: A) Zero B) Non-Zero

+Q +Q Point X

CPS Question

Drawn are a set of equipotential lines. Consider the electric field at points A and B. Which of the following statements is true?

0V 10V 20V 30VPoint A

Point B

A) |EA| > |EB| B) |EA| < |EB| C)|EA| = |EB| D)Not enough information given. E) None of the above

32

CPS Question

Two charges, +Q and -Q, are fixed in space. The electric field at the point X midway between the charges is: A) Zero B) Non-Zero

+Q -Q Point X

Point P

The magnitude of the electric field at point P is: A) Zero B) Non-Zero

The magnitude of the voltage at point P is: A) Zero B) Non-Zero

All points on conductor must be at the same

electrical potential.

Imagine point a at Voltage V a .

Since E=0 everywhere inside the conductor (no steepness), integral to

point b is always 0. V ab =0.

E. Potential inside conductors