physics - giancoli 7e ch 17: electric...

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PHYSICS - GIANCOLI 7E

CH 17: ELECTRIC POTENTIAL

CONCEPT: ELECTRIC POTENTIAL ENERGY

● If you release 2 charges, they move → gain ________________________

- Two charges have a “stored” energy → ________________________

- ENERGY CONSERVATION: −𝚫𝐔 = 𝚫𝐊

- Be careful! Decreases 1 r⁄ , not 1 r2⁄

- The signs of the charges & energy DO matter

EXAMPLE: How far apart must a 3 µC and a –2 µC charge be so that their potential energy is –100 mJ? ● Potential energy for a GROUP OF CHARGES:

- 𝐔𝐓𝐎𝐓 = _____________________ - This is the energy needed to separate each charge _____________. EXAMPLE: How much potential energy is carried by the following system of charges?

● Electric potential energy between TWO POINT CHARGES:

→ 𝐔 = ________

q1

q2

r

1 C -2 C

3 C

3 m

4 m



CONCEPT: ELECTRIC POTENTIAL

● ELECTRIC POTENTIAL, also called simply POTENTIAL, is related to, but different from Electric Potential ENERGY.

● The UNIT of Electric Potential is the ______________ (𝐕 =1J

1C⁄ )

- CAREFUL! V is the symbol for both Electric Potential AND its unit. Example: __________

EXAMPLE: A 5C and 3C charge are separated by some distance. If the 5C charge feels 200 V from the 3C charge, what is the potential energy of the 5C charge?

FIELD → FORCE POTENTIAL → ENERGY

- A single charge produces an Electric FIELD - Field tells charges how much ______________ to feel

- Once there’s a second charge, there is _____________

→ 𝐅 = 𝐪 𝐄

- E is the strength of the ____________ field

- q is the [ PRODUCING | FEELING ] charge

→ “Electric FIELD” E = FORCE Field

- A single charge also produces an Electric POTENTIAL - Potential tells charges how much ___________ to have

- Once there’s a second charge, there is _____________

→ U = _______

- V is the strength of the ____________ field

- q is the [ PRODUCING | FEELING ] charge

→ “Electric POTENTIAL” V = ENERGY Field



CONCEPT: MOVEMENT OF CHARGES IN POTENTIAL FIELDS

● [ + | - ] charges ALWAYS move to low potential, and [ + | - ] charges ALWAYS to high potential.

- Potential is a field that provides “motivation” for charges to move → gives them potential energy EXAMPLE: An electron is at rest between two points, A at 10 V, and B at 0 V. Which point will the electron move to? EXAMPLE: A metal rod is placed in a uniform electric field as shown below. Which end of the rod is at a higher potential?

______ ______



CONCEPT: POTENTIAL DUE TO A POINT CHARGE

● Remember: Electric POTENTIAL (POTENTIAL) is an ENERGY field → U = q V → V = _________

→ So we think of POTENTIAL as Electric Potential Energy per ___________________________.

● This means that a charge q either gains or loses energy through a potential difference.

→ 𝚫𝑼 = _________

EXAMPLE: a) What is the potential 0.5 m away from a 2C charge? b) What about 1 m away? c) What is the potential

difference from P1 to P2? The voltage?

→ Remember: Voltage is ______, not ______!

● A POINT CHARGE produces a Potential:

- V = _______ - Units are VOLTS (1 V) ● Potential DIFFERENCE → difference in potential between 2 points = __________ (aka _______________) - CAREFUL! Voltage ______ Volts ● Potential DIFFERENCE measured from Point A to Point B → ______ = ____________

q

P1 P2



PRACTICE: ELECTRIC POTENTIAL DUE TO A POINT CHARGE

How far from a 5 C charge will the potential be 100 V?



PRACTICE: POTENTIAL BETWEEN TWO POINT CHARGES

A -1 C and a 5 C charge lie on a line, separated by 5cm. What is the electric potential halfway between the two charges?



EXAMPLE: POTENTIAL DIFFERENCE BETWEEN TWO CHARGES

Two charges, q and -3q, lie on a line as shown below. What is the potential difference between point A and point B?

s

x x

q -3q

A B



CONCEPT: WORK DUE TO ELECTRIC FORCE

● Whenever a charge moves, it changes its position → so its [ POTENTIAL | KINETIC ] energy changes.

- The Electric Force and/or Field accelerates and moves charges.

- Remember: whenever there’s a change in energy, some ___________ is done.

● Work by the electric force depends ONLY on ____________________________________ , NOT the “path”.

- When charges get “very far away” (infinitely far), Electric Potential Energy → _____.

EXAMPLE: A 2nC charge is initially 5mm away from a 10nC charge. The 2nC charge is then moved 2mm closer to the

10nC charge. What is the work done by the electric force?

EXAMPLE: A 1C charge is placed in a horizontal, uniform electric field of magnitude 1,000 N/C. a) What is the work done on the charge when it travels a distance of 2m at an angle of 30o below the horizontal? b) If this 3g charge initially starts from rest, how fast is this charge going after the 2m displacement?

● Energy conservation: −ΔU = Δ𝐾

- Work energy theorem: 𝑊 = Δ𝐾

→ 𝑊 = ___________

- U & V relationship: Δ𝑈 = 𝑞Δ𝑉

→ 𝑊 = ___________ → 𝑊 = _____________ 𝑊 = ___________

q1

q2 �⃗�

q



PRACTICE: WORK DUE TO POTENTIAL DIFFERENCE

An electron moves from point A to point B. The potential difference between these two points is 100 V. What is

(a) the point of higher potential?

(b) the work done on the electron?

(c) the final speed of the electron if its initial speed is zero?



EXAMPLE: BRINGING TWO CHARGES FROM INFINITY

How much work is done by the electric force in bringing a 5C charge from infinitely far away to the origin of a coordinate

system, and then bringing a -2C charge from infinitely far away to a point (3m, 4m)? Assume there are no other charges.



PRACTICE: WORK TO ASSEMBLE A TRIANGLE OF CHARGES

What work is needed to assemble an equilateral triangle of side length 5 cm, with a 5 C charge at each vertex?

5 cm

5 cm 5 cm



EXAMPLE: SPEED OF ELECTRON IN UNIFORM ELECTRIC FIELD

An electron is initially at rest in a uniform, 500 N/C electric field. After traveling 10 cm, what is the electron’s speed?



CONCEPT: RELATIONSHIPS BETWEEN FORCE, FIELD, ENERGY, POTENTIAL

● So far we have seen FOUR related terms with similar NAMES and EQUATIONS. Now let’s put it all together:

r 2 r

q1 q2

ELECTRIC FORCE

𝑭 = 𝒌𝒒𝟏𝒒𝟐

𝒓𝟐

ELECTRIC POTENTIAL ENERGY

𝑼 = 𝒌𝒒𝟏𝒒𝟐𝒓

q

ELECTRIC FIELD

(ELECTRIC FORCE FIELD)

𝑬 = 𝒌𝒒

𝒓𝟐

ELECTRIC POTENTIAL (POTENTIAL)

(ELECTRIC ENERGY FIELD)

𝑽 = 𝒌𝒒

𝒓

→ Remember:

- Electric Potential DIFFERENCE = Potential Difference = VOLTAGE = Δ𝑉

- Electric Potential ENERGY difference = −Δ𝑈 = “WORK”



EXAMPLE: POTENTIAL AT CENTER OF CHARGES ARRANGED IN A SQUARE

What is the potential at the center of the arrangement shown in the following figure?

PRACTICE: POTENTIAL AT CENTER OF CHARGES ARRANGED IN A CIRCLE

4 identical charges are arranged so that they are evenly spaced in a circle. If the radius of the circle is 10 cm, and the potential at the center of the circle is –100 V, what is the magnitude of each charge?

5 mm

5 mm

1 nC

2 nC

-3 nC

-1.5 nC



PRACTICE: POTENTIAL DIFFERENCE DUE TO A POINT CHARGE

A -2 C charge lies at rest. a) What is the potential difference between point A, which is 1.5m from the charge, and point B,

which is 4m from the charge? b) What would the work on a 4 C charge be to move it from A to B?

EXAMPLE: POTENTIAL DIFFERENCE DUE TO TWO CHARGES

A 5 nC charge and a -3 nC charge lie on a line, separated by 6 mm. a) What is the potential halfway between the two

charges on the line connecting them? b) What is the potential halfway between the charges, but 4 mm above the line

connecting them? c) How much work would it take to move a 1 nC charge from the first point to the second?

PRACTICE: STOPPING A POINT CHARGE

A 5 g, 3 µC point charge is moving with an initial speed of 20 m/s away from a –5 µC charge. If they are initially 5 cm apart,

how far can the 3 µC travel before stopping?



CONCEPT: THE ELECTRONVOLT ● Suppose two plates of equal & opposite charge have a potential difference of 1V →

- Electron moves from one plate to another, the potential difference is ___________

→ Change in Potential Energy is _________________________ ( _____ → _____ ) ● 1 eV is called an ELECTRONVOLT

→ 1 eV = (1.6 × 10−19C)(1V) = 1.6 × 10−19J

- Electronvolt = Change in potential energy of ONE electron through ONE volt.

- Just a different unit of energy for small charges!

EXAMPLE: What is the speed of an electron with 150 eV of kinetic energy?

1 V

+ -



CONCEPT: EQUIPOTENTIAL SURFACES

● EQUIPOTENTIAL SURFACES are surfaces of _________________ potential. ● Relationship between electric field and potential → 𝐄 = __________ → Electric field only exists where potential is changing.

→ �⃗� is ALWAYS _________________ to equipotentials, points along [ INCREASING | DECREASING ] ΔV ● Work along equipotential surface = _______________ - Because 𝐖 = −𝐪𝚫𝐕 → No 𝚫𝑽, no 𝑾 ● Equipotential surfaces of a POINT CHARGE: ● Equipotential surfaces of a DIPOLE:

EXAMPLE: What is the distance from a 1 C point charge to an equipotential surface of 150 V?



EXAMPLE: ELECTRIC FIELD DUE TO EQUIPOTENTIAL SURFACES

What is the magnitude and direction of the electric field due to the equipotential surfaces shown in the following figure?

PRACTICE: DRAWING EQUIPOTENTIAL SURFACES FROM ELECTRIC FIELD LINES

Draw the electric field that corresponds to the equipotential surfaces shown in the following figure. Note that the potential is decreasing in the upward direction.

60o

10 V

15 V 20 V

y

x



CONCEPT: CAPACITORS AND CAPACITANCE

● CAPACITOR: Two nearby surfaces of _________&____________ charge → stores [ POTENTIAL | KINETIC ] energy

● Connecting a capacitor to a battery produces a simple CIRCUIT

- “Source” of moving charges comes from a __________________

- Voltage of battery = voltage of capacitor

● CHARGE on capacitor → 𝑄 = _____

- CAPACITANCE (C) measures the ___________ of the capacitor.

- Larger capacitance → [ LARGER | SMALLER ] the charge stored

EXAMPLE: What is the charge on the capacitor in the following figure?

● CAPACITANCE is defined as 𝐶 = __________ - Units are F (Farads)

9 V

3 F

Battery Capacitor

CIRCUIT



CONCEPT: PARALLEL PLATE CAPACITORS

- Electric Field BETWEEN plates is ______________.

- Electric Field OUTSIDE plates is ______________.

● The magnitude of the UNIFORM Electric Field within a capacitor: 𝐄 = _______ → 𝐄 =𝐐

𝛜𝟎𝐀

● Equipotential surfaces between plates: EXAMPLE: A parallel plate capacitor has an area of 5 cm2, a plate separation of 10 mm, and a voltage across the plates of 100 V. a) What is the charge of the capacitor? b) What is the magnitude of the electric field between the plates?

+Q

-Q Electric Field

Equipotential

Surfaces

● Capacitance for ANY Capacitor is → C = Q / V

● Capacitance for PARALLEL PLATE Capacitor is: → C = __________

- A is area, d is distance between plates, 𝜖0 = 8.85 × 10−12 [𝐹

𝑚]



PRACTICE: CAPACITANCE OF PARALLEL CIRCULAR PLATES

Two circular plates of radius 2cm are brought together so their separation is 5mm. What is the capacitance of these plates? EXAMPLE: POINT CHARGE IN CAPACITOR

Two 1 cm by 1 cm plates, separated by 10 mm, form a capacitor. If each plate is charged to 30 nC, (a) What is the potential difference between the plates? (b) What is the electric field between the plates? (c) How much energy does it take to move a – 5 nC charge from the positive plate to the negative plate? PRACTICE: CHARGING A CAPACITOR

A 3 F capacitor is given a potential difference across its plates of 10 V. What is the charge built up on its plates? If the source of the potential difference across the plates is removed, but the plates maintain their charge, what is the new potential difference across the capacitor if the distance between the plates is doubled?



CONCEPT: ENERGY STORED BY CAPACITOR

● Remember: Capacitors separate charges, and this separation leads to potential energy stored. But HOW MUCH energy?

● ENERGY DENSITY (𝑢) = Energy per unit volume → 𝒖 = __________ - Volume of a parallel plate capacitor → 𝒗𝒐𝒍𝒖𝒎𝒆 = __________ → 𝒖 = __________ = ___________ EXAMPLE: Two parallel plates of area 50 cm2, with a separation of 10 mm, have a voltage across them of 20 V. What is the energy stored? The energy density? EXAMPLE: What is the strength of the electric field in a capacitor storing 2.5 mJ per cubic-centimeter?

● Energy stored by ANY capacitor → 𝐔 = _________ = __________ = _________ - Use Q = CV to change between all 3 forms



PRACTICE: DEFIBRILLATOR

A cardiac defibrillator can be modeled as a parallel plate capacitor. When it is charged to a voltage of 2 kV, it has a stored energy of 1 kJ. What is the capacitance of the defibrillator? PRACTICE: ENERGY RELEASED BY FLASHBULB

Typically, a flashbulb will have a capacitance of 1000 mF. If the bulb were charged to a voltage of 500 V, how much energy is released when the flash goes off, if the bulb loses 80% of its charge in a single flash?



CONCEPT: INTRO TO DIELECTRICS

● Dielectric: Insulator between charged plates [ INCREASES | DECREASES ] capacitance: 𝐶 = 𝜅𝐶0

- DIELECTRIC CONSTANT ≥ 1 (no units!)

- Always [ STRENGTHEN | WEAKEN ] Electric Fields → 𝐸 = 𝐸0/𝜅

CONSTANT CHARGE (Q) CONSTANT VOLTAGE (V)

- No battery connected

- 𝑄 = 𝐶 𝑉 → V ___________

- 𝑈 =1

2𝑄2 / 𝐶 → U ___________

- 𝑢 =1

2𝜖0𝐸2 → u ___________

- Inserted when battery still connected

- 𝑉 = 𝑄 / 𝐶 → Q ___________

- 𝑈 =1

2𝐶 𝑉2 → U ___________

- 𝑢 =1

2𝜖0𝐸2 → u ___________

EXAMPLE: A capacitor is connected to a battery as shown below. What is the charge on the capacitor after a dielectric (𝜅 = 2) is inserted into the capacitor while it is still connected to the battery?

9 V

3 F



EXAMPLE: CAPACITOR WITH A DIELECTRIC

A capacitor in a vacuum is charged to 64V between its plates, then disconnected. Initially, each plate has 32μC. An

insulating slab of dielectric glass with = 3 is placed between the plates. a) What is the capacitor’s new capacitance? b) What is the new voltage across the capacitor? PRACTICE: CIRCULAR PLATE CAPACITOR WITH DIELECTRIC

A parallel plate capacitor is formed by bringing two circular plates, of radius 0.5 cm, to a distance of 2 mm apart. The capacitor is made so that it has a dielectric of constant 𝜅 between the plates. When the charge on the capacitor is 3 nC, the voltage of the capacitor is 5000 V. What is the dielectric constant? EXAMPLE: CAPACITORS PARTIALLY FILLED WITH DIELECTRIC

What is the new capacitance of the two capacitors that are partially filled with dielectrics shown in the following figure?

(a) (b)

A

d/2

d/2

𝜅

A

d

L/2

𝜅

L/2



CONCEPT: HOW DIELECTRICS WORK ● A DIELECTRIC is an insulating material that can ______________________

- At the atomic level:

● Dielectrics [ INCREASE / REDUCE ] electric field strength within capacitors

Alone In external 𝐸

+ -

+ -

+ -

+ -

+ -

+ - + -

+ - + -

+ - + -

____________ ____________

+

+

+

-

-

-

+Q -Q



physics - giancoli 7e ch 17: electric...

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