Chapter 17

Electric Potential Energy and the

Electric Potential

Calculate the change of PEg for:

a) A 10.0 kg object falling 10.0 mb) A 5.0 kg object falling 10.0 m

Calculate the change of PEg per massfor each object.

Make a conclusion: what does this ratio depend on? What does it characterize?

Which force is doing work on the ball? Is the work positive or negative? Does it lead to increase or decrease of potential energy?

Analogy

Which force is doing work? Which energy is changing? Is the energy increasing or decreasing?

Analogy

Gravitational field’s strength Electric field’s strength

What characterizes the object What characterizes the object

What characterizes the motion What characterizes the motion

Analogy

Formula for Formula for

White Board Practice1. Draw a uniform electric field. E = ___________.2. Make up two positive charges and place them in the field.3. Let them travel __________ cm. 4. Calculate the change in EPE for each charge.

5. Calculate the ratio

DEFINITION OF ELECTRIC POTENTIAL DIFFERENCE

Potential difference – ratio of the change of EPE per charge

SI Unit of Electric Potential: joule/coulomb = volt (V)

DEFINITION OF ELECTRIC POTENTIALPotential difference – ratio of EPE per charge

BACK TO THE BOARD1. Return the two charges to their original position in the field.2. Mark that point with a V1 to indicate potential at that point3. Mark a place 10.0 cm down the direction of the field. Mark it with V2

4. For each charge, calculate a) Change of EPEb) Potential difference between V1 and V2

c) Compare the magnitudes of V1 and V2 (which one of them is greater)

What is the natural direction of a positive charge moving in an electric field: - in the direction of the field / - opposite the direction of the field- towards a lower potential / towards a higher potential

White Board Practice1. In the center of the field, place a positive and a negative charge (make up

their magnitudes).2. Show the direction of the electric force on each charge.3. Allow the force move the charge 5.0 cm.4. Calculate the change of EPE for each charge.5. Calculate potential difference that each charge naturally went through.

Conclusion:1. EPE characterizes _________________________ (charge or field)

2. Potential characterizes ______________________ (charge or field)

3. ______________________ force works on charges as they move in EF

4. As charges move in an electric field naturally, their EPE _______________

5. If EPE increases, __________________ force has worked on the charge

6. Positive charges naturally move towards ___________________ potential

7. Negative charges move towards _____________________ potential.

Check your understanding

+

+

A +5.0 nC charge moves 5.0 cm at a 60-degree angle to the direction of the field.Calculate the change in its potential energy.

ReviewCharges have _________________________ associated with their position in an ____________________________

Charges that are moving naturally in an ____________________, lose / gain _______________________________

_____________________ characterizes the charge

Ratio of __________________ per charge is called _____________________

Ratio of ___________________ per charge is called __________________________________________________

Positive charge naturally moves through a _____________________________

Negative charge naturally moves through a ____________________________

Unit Play

Potential in EF of a point chargeWhite board practice:

+ 5.0 C

1.0 m

2.0 m

1. Find the magnitude of the field at point A and at point B.2. Potential energy of a +2.0nC charge at each point (refer to the analogy with PEg)3. Find the change of EPE as the charge moves

A B

Potential in EF of a point chargeWhite board practice:

+ 5.0 C

1.0 m

2.0 m

1. Determine potential difference between the two points.2. Make a conclusion about the potential (magnitude) as the distance to the

charge increases / decreases.3. As you get closer to the positive charge, V is ______________________4. As you move away from the positive charge, V is ___________________

A B

Potential in EF of a point chargeWhite board practice:

- 5.0 C

1.0 m

2.0 m

1. Find the magnitude of the field at point A and at point B.2. Find the change of EPE for a +2nC charge as it moves:

A B

Potential in EF of a point chargeWhite board practice:

- 5.0 C

1.0 m

2.0 m

1. Determine potential difference between the two points.2. Make a conclusion about the potential (magnitude) as the distance to the

charge increases / decreases.3. As you get closer to the positive charge, V is ______________________4. As you move away from the positive charge, V is ___________________

A B

Deriving the formula for potential near a point charge

Potential around a positive charge is _________________

Potential around a negative charge is ________________

Potential is a scalar!

2.0 m

Find the potential midway between the two charges:

a) +2.0 nC and – 4.0 nCb) -2.0 nC and +4.0 nCc) -6.0 nC and +6.0nC

Midpoint problems revisited

2.0 m

Is there a net force on the point between the two charges?Is there a net field between the two charges?Is there a net potential between the two charges?

Zero V vs. ES equilibrium

Midpoint problems revisited

2.0 m

If you know the net field between the charges, you can predict

_________________________________________________________________

If you know the net potential between the charges, you can predict

_________________________________________________________________

EPE of a system of ChargesDoes a singular electric charge have EPE if there is no other charge or EF in the proximity? Explain

Consider two charges:

+5nC

+2nC

A +5.0 nC charge is fixed in pace.What would be the EPE of the system of these two charges?How much work would need to be done to bring another +2.0 nC form an infinitely far-away point to 1.0 m proximity of the charge?

Whose EPE is this?

+5nC+2nC

Think gravity

Potential energy – energy of the system of two objects (charges)

p. #26(textbook)Four identical charges (+2.0 μC each) are brought from infinity and fixed to a straight line. The charges are located 0.40 m apart. Determine the electric potential energy of this group.

p. 27 (textbook)

Let’s start with +8.00 μC

- 15.0 μC moves in. Predict: did PE of the system rise or drop?

+20.0 μC moves in. Predict: did PE of the system rise or drop?

Determine the electric potential energy for the array of three charges shown in the drawing, relative to its value when the charges are infinitely far away.

An equipotential surface is a surface on which the electric potential is the same everywhere.

r

kqV

The net electric force does no work on a charge as it moves on an equipotential surface.

s

VE

The plates of the capacitor are separated by a distance of 0.032 m, and the potential difference between them is VB-VA=-64V. Between the two equipotential surfaces shown in color, there is a potential difference of -3.0V. Find the spacingbetween the two colored surfaces.

mV100.2m 0.032

V 64 3

s

VE

m105.1mV100.2

V 0.3 33

E

Vs

A charged sphere

A charged sphere is handled like an equipotential sphere around a point charge, providing V∞=0

r

kqV

Consider two spheres: both are missing 5.0x1013 eR1 = 15 cm, R2 = 30 cm

Predict the ratio of V1/V2

Find it mathematically, using numbers.

A charged sphere

What would happen IF these two spheres were connected with a wire?

Find the final charge on of each sphere