a difference in electrical potential between the upper atmosphere and the ground can cause...

A difference in electrical potential between the upper atmosphere and the ground can cause electrical discharge (motion of charge).

Ch 25 – Electric PotentialCh 25 – Electric Potential

Ch 25 – Electric PotentialCh 25 – Electric Potential

So far, we’ve discussed electric force and fields.

Now, we associate a potential energy function with electric force.

This is identical to what we did with gravity last semester.

gravity electricity

rr

mmGFg ˆ

221

rr

qkE e ˆ

2

r

r

mGg ˆ

2

221

r

qqkF ee

r

mmGU g

21 ?

Ch 25.1 – Electric Potential and Potential DifferenceCh 25.1 – Electric Potential and Potential Difference

• Place a test charge, q0, into an E-field. The charge will experience a force:

EqF

0• This force is a conservative force.

• Pretend an external agent does work to move the charge through the E-field.

• The work done by the external agent equals at least the negative of the work done by the E-field.


• Let’s introduce a new symbol:

sd

• We’re talking about moving charges through some displacement.

• The “ds” vector is a little tiny step of displacement along a charge’s path.


• If q0 moves through the E-field by a little step ds, the E-field does some work:

sdFdW

fieldE

• As the E-field performs this work, we say that the potential energy of the charge-field system changes by this amount.

• This is the basis for our definition of the potential energy function.


• If q0 moves through the E-field by a little step ds, the E-field does some work:

sdFdW

fieldE

sdEqsdFdWdU

0fieldE

B

A

AB sdEqUUU

0


B

A

AB sdEqUUU

0

The change in electrical potential energy of a charge-field system as the charge moves from A to B in the field.

The integral accounts for the motion of the charge through a 1-D path. It’s called a “path” or “line” integral.


B

A

AB sdEqUUU

0


Because electric force is conservative, the value of the integral does not depend on the path taken between A and B.


B

A

AB sdEqUUU

0


Potential Energy refresher:

Potential Energy measures the energy a system has due to it’s configuration.

We always care about changes in potential energy – not the instantaneous value of the PE.

The zero-point for PE is relative. You get to choose what configuration of the system corresponds to PE = 0.


• What we’re about to do is different than anything you saw in gravitation.

• In electricity, we choose to divide q0 out of the equation.

• We call this new function, ΔV, the “electric potential difference.”

B

A

sdEq

UV

0


• This physical quantity only depends on the electric field.

• Potential Difference – the change in potential energy per unit charge between two points in an electric field.

• Units: Volts, [V] = [J/C]

B

A

sdEq

UV

0

Potential difference between two points in an Electric Field.


• Do not confuse “potential difference” with a change in “electric potential energy.”

• A potential difference can exist in an E-field regardless the presence of a test charge.

• A change in electric potential energy can only occur if a test charge actually moves through the E-field.

B

A

sdEq

UV

0

Potential difference between two points in an Electric Field.


• Pretend an external agent moves a charge, q, from A to B without changing its speed. Then:

But:

UW

0q

UV

VqW


• Units of the potential difference are Volts:

• 1 J of work must be done to move 1 C of charge through a potential difference of 1 V. J/C 1 V 1


• We now redefine the units of the electric field in terms of volts.

V/m 1 N/C 1 E-field units in terms of volts per meter


• Another useful unit (in atomic physics) is the electron-volt.

• One electron-volt is the energy required to move one electron worth of charge through a potential difference of 1 volt.

• If a 1 volt potential difference accelerates an electron, the electron acquires 1 electron-volt worth of kinetic energy.

J101.60VC101.60 eV 1 -19-19 The electron-volt

Points A and B are located in a region where there is an electric field.

How would you describe the potential difference between A and B? Is it negative, positive or zero?

Pretend you move a negative charge from A to B. How does the potential energy of the system change? Is it negative, positive or zero?

Quick Quiz 25.1Quick Quiz 25.1

Let’s calculate the potential difference between A and B separated by a distance d.

Assume the E-field is uniform, and the path, s, between A and B is parallel to the field.

Ch 25.2 – Potential Difference in a Uniform E-FieldCh 25.2 – Potential Difference in a Uniform E-Field

B

A

sdEV

Let’s calculate the potential difference between A and B separated by a distance d.

Assume the E-field is uniform, and the displacement, s, between A and B is parallel to the field.

B

A

dsEV


EdV

B

A

sdEV

B

A

EdsV cos1

The negative sign tells you the potential at B is lower than the potential at A.

VB < VA

Electric field lines always point in the direction of decreasing electric potential.


EdV

Now, pretend a charge q0 moves from A to B.

The change in the charge-field PE is:

If q0 is a positive charge, then ΔU is negative.

When a positive charge moves down field, the charge-field system loses potential energy.


EdqVqU 00

Electric fields accelerate charges… that’s what they do.

What we’re saying here is that as the E-field accelerates a positive charge, the charge-field system picks up kinetic energy.

At the same time, the charge-field system loses an equal amount of potential energy.

Why? Because in an isolated system without friction, mechanical energy must always be conserved.


If q0 is negative then ΔU is positive as it moves from A to B.

When a negative charge moves down field, the charge-field system gains potential energy.

If a negative charge is released from rest in an electric field, it will accelerate against the field.


EdqVqU 00

Consider a more general case.

Assume the E-field is uniform, but the path, s, between A and B is not parallel to the field.


B

A

sdEV

Consider a more general case.

Assume the E-field is uniform, but the path, s, between A and B is not parallel to the field.


sEsdEsdEVB

A

B

A

sEqVqU

00


sEV

If s is perpendicular to E (path C-B), the electric potential does not change.

Any surface oriented perpendicular to the electric field is thus called a surface of equipotential, or an equipotential surface.

The labeled points are on a series of equipotential surfaces associated with an electric field.

Rank (from greatest to least) the work done by the electric field on a positive charge that moves from A to B, from B to C, from C to D, and from D to E.

Quick Quiz 25.2Quick Quiz 25.2

A battery has a specified potential difference ΔV between its terminals and establishes that potential difference between conductors attached to the terminals. This is what batteries do.

A 12-V battery is connected between two plates as shown. The separation distance is d = 0.30 cm, and we assume the E-field between the plates is uniform. Find the magnitude of the E-field between the plates.

EG 25.1 – E-field between to plates of chargeEG 25.1 – E-field between to plates of charge

A proton is released from rest at A in a uniform E-field of magnitude 8.0 x 104 V/m. The proton displaces through 0.50 m to point B, in the same direction as the E-field. Find the speed of the proton after completing the 0.50 m displacement.

EG 25.1 – Proton in a Uniform E-fieldEG 25.1 – Proton in a Uniform E-field

a difference in electrical potential between the upper atmosphere and the ground can cause...

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