G Notes - 4-1 Electrostatics Sub-Unit.pdf

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4.1.1 Elementary Charge

Atomic Structure Review

Definitions

• charge – a fundamental property of matter

– measured in __________________ or __________________________ • charge on an object is carried by particles:

– __________________

• ______________________ • ______________________ – __________________

• ______________________ • ______________________

Charged Objects

• Objects are normally electrically __________________ (same number of protons and electrons)

– measured in __________________ or __________________________

Example #1

• An object has three excess electrons

– What is its “elementary charge”? ____________ – What is its charge in coulombs?

Example #2

• An object has 75 protons and 65 electrons.

– What is its “elementary charge”? ____________ – What is its charge in coulombs?

Law of Conservation of Charge

The total amount of charge in a closed system remains constant – charge is not created or destroyed, it only moves from one object to another

Charge “moves” as a result of ELECTRON movement ONLY!!!

nucleus two types of nucleons ___________ + charge ___________ 0 charge

Nucleons are not allowed to move around WITHIN matter

_____________ negative charge Only subatomic particles that are allowed to move around WITHIN matter

electrons lack of

electrons

excess electrons

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Example #3

• A metal sphere with two excess electrons touches a neutral metal sphere and is then taken away.

– What is do you predict the charge on each sphere will be after they make contact?

– What is the total charge on both spheres after they come in contact?

PRACTICE

1) A metallic sphere gains 500 electrons. What is the charge on the sphere in coulombs?

2) How many electrons does it take to generate -3.5 coulombs of charge?

3) Which of the following charges is allowable in the ‘real world’? a. 4.8 x 10-16 C

b. 3.5 e c. 500 e d. 9.92 x 10-17 C e. 1.5 x 103 e f. 1.6 x 10-20 C

.

Review Questions

4.1.1 – Convert between elementary charge and charge in coulombs. Determine if a charge is possible. Determine how charge will be distributed in conservation of charge problems.

- What is the charge on an object with four excess electrons?

[-4e; 6.4 x 10-19 C] - What is the charge on an object that contains 35 electrons and 85 protons?

[+50; 8.0 x 10-18 C] - Which set of particles would produce a charge of +3.2 x 10-18 coulombs?

(1) 400 electons and 200 protons (2) 40 electrons and 20 protons (3) 200 electrons and 400 protons (4) 20 electrons and 40 protons

[4] - Which charges could NOT exist on a real-world object?

(a) 3.2 x 10-19 C (e) 0.5 x 10-19 C (b) 6.5 C (f) 3.2 x 10-21 C (c) -20 e (g) 3.5 e

(d) 1.2 x 102e (h) 1.6 x 10-19e

[e, f, g, h] - Object A begins with a charge of -3.0 coulombs; object B begins with a charge

of -7.0 coulombs; and object C begins with no charge. Object A is touched to object B then removed. Object B is then touched to object C and removed. What is the final charge on each of the three objects?

[A = -5.0C; B = -2.5C; C = -2.5C]

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4.1.2 Transfer of Charge

Conductive Properties of Materials

Charging by Friction

• Rub two insulators together

– _________________ move from one to the other

– One object becomes ________ the other _________

RULE #1 – ________________________________________________

Grounding

• Since the Earth is very large it can neutralize:

– negative objects by ____________________ electrons

– positive objects by _____________________ electrons

RULE #2 – _______________________________________________

Induction

induction – movement of charge _______________________

Negative Rod

Positive Rod

RULE #3 – ________________________________________________

RULE #4 – ________________________________________________

1 2 3

HIGH CONDUCTIVITY LOW RESISTIVITY

LOW CONDUCTIVITY HIGH RESISTIVITY _______________________

_______________________ Allows electrons to flow freely

_______________________ _______________________ Strongly resists flow of electrons

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Conduction

conduction – movement of charge _______________________

Negative Rod

Positive Rod

RULE #5 – ________________________________________________

Electroscope

Induction

Negative Rod

Positive Rod

Charging by Conduction

Negative Rod

Positive Rod

Charging by Induction

1 2 3 4 5

1 2 3

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Positive Rod

RULE #6 – ________________________________________________

PRACTICE

1) A rubber balloon is rubbed on a person’s hair. a. Explain how the balloon becomes charged.

b. Sketch a diagram of the charge distribution when the balloon is stuck to a wall.

2) A metal sphere with a charge of -3 coulombs is brought into contact with a metal sphere with a charge of +5 coulombs.

a. Draw an arrow between the two spheres in the “Before” picture to show the direction in which electrons will flow when the spheres touch. b. Determine the charge on each of the two pith balls after they come into

contact, then are separated.

3) A metal sphere with a charge of +16 coulombs is brought into contact with a metal sphere with a charge of +4 coulombs.

a. Draw an arrow between the two spheres in the “Before” picture to show the direction in which electrons will flow when the spheres touch. b. Determine the charge on each of the two pith balls after they come into

contact, then are separated.

Testing Electroscopes

+16 C +4 C

Before After

1 2 3 4 5 6

-3 C +5 C

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- Object A is negatively charged and is used to charge object B by conduction. What is the final charge on objects A and B?

[A -; B -] - Object A is negatively charged and is brought near neutral object B without

touching it. What is the final charge on objects A and B?

[A -; B=0] - Object A is negatively charged and is used to charge object B by induction.

What is the final charge on objects A and B?

[A -; B +] - A small object is tested to determine its charge. What test could be used to

prove that the object is positively charged? What test could be used to prove that the object is not charged?

[repelled from + attracted to + AND -]

- A negatively charged rod is brought near a neutral electroscope then removed, what is the reaction of the electroscope leaves?

-[diverge then converge] - A negatively charged rod is brought near a charged electroscope causing its

leaves to converge. What is the charge on the electroscope?

[+] - A negatively charged rod is brought near a charged electroscope causing its

leaves to diverge. What is the charge on the electroscope?

[-]

4.1.2 – Determine the direction in which electrons flow. Explain the process of conduction, induction, and charging by induction. Explain the rules for testing an object to determine its charge. Explain how an uncharged object will react to the presence of a charge one. Explain how electroscopes become charged and how to test them.

- In which direction will electrons flow in each case?

[; ; ; ]

-3C -6C +3C -6C

-4C +5C +8C +2C

a.

b.

c.

d.

+

-

+

-

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4.1.3 Coulomb’s Law

Electrostatic Force

• Same charges repel

• Opposite charges attract

• Amount of force depends on:

– ______________________________________________________________

Electrostatic vs. Gravitational Force

• Consider two electrons that are 1.0 micrometer apart.

– Gravitationally ______________________

– Electrostatically _____________________ - Which of the following shows an electroscope being charged negatively by

conduction?

[C] - Which of the following electroscopes could be charged positively by induction?

[F] - In which of the following are the leaves of the electroscope negatively

charged?

[C; D; E]

[; ; ; ]

+ + + + +

– – – – –

A B C D

+ + + + +

E F

– – – – – _r

Fe

Equation

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Example #1

• Determine the electrostatic force between an object with a +2.0 coulomb charge and an object with a -2.0 coulomb charge if they are separated by 2.0 meters.

Example #2

• Determine the electrostatic force between an object with -2.0 micro-coulombs of charge and an object with -5.0 micro-coulombs of charge if they are separated by 5.0 nanometers.

PRACTICE

1) When two spheres, each with charge Q are positioned a distance R apart, they are attracted to one another by a force of magnitude F. What force would they be attracted by if…

a. …one of the charges is tripled while the other is doubled?

b. …the separation distance is changed to 3R?

c. …one of the charges is changed to Q/2?

d. …one of the charges is doubled and the separation distance is R/2?

4.1.4 Electric Fields

Electric Field Maps

• Electric fields…

– exist near __________________________________________

– mapped using a ______________________ test charge

• 1 – place test charge

• 2 – draw arrow in direction pushed

• 3 – this is the field direction

4.1.3 – Use equation to determine electrostatic force; charge; and/or distance. Determine the effects of changing parameters on strength of electrostatic force.

- Determine the electrostatic force that a +4.0 coulomb charge exerts on a -6.0 coulomb charge when 2.0 meters apart.

[5.4 x 1010_N]

- If two charged objects are attracted to one another by an electrostatic force of 5.0 newtons, what force would they be attracted by if the charge on both of them were doubled?

[20N] - An electrostatic force F acts between two objects with charges +q and +q when they are a distance R apart. If the distance between the objects is halved, the electrostatic force would become

(1) F/2 (2) F/4 (3) 2F (4) 4F

[4]

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Electric Field Strength

• Field strength…

– Gets _____________________ with distance

– __________________ exerted per unit ______________________

Example #1

• An object with a charge of -2.0 coulombs positioned in a uniform electric field experiences a force of -300 newtons. What is the strength of the electric field?

Example #2

• What is the force experienced by a 0.05 coulomb charge when it is placed in an electric field with a strength of 3.0 x 103 newtons per coulomb?

Parallel Plates

– Between plates

• E  Fe = _______________________________________ – Outside plates = ____________________

+

A

B C

r E

Equation

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Hollow Charged Sphere

– Normal field pattern outside

– ___________________ inside

PRACTICE

1) An electron is placed within a uniform electric field with strength of 5.0 x 10-8 newtons per coulomb.

a. Calculate the electrostatic force that is experienced by the electron.

b. Calculate the acceleration of the electron. [electron mass = 9.11 x 10-31 kg]

2) An electron is fired from a point outside two parallel, oppositely charged plates into the region between the plates. Sketch the path of the electron as it moves between the plates and comes out the other side. [Hint: which plate will the electron be deflected toward?]

3) An object with a charge of -4 x 10-3 coulombs is placed between a set of oppositely charged, parallel plates. The object experiences a force of 5 x 10-6 newtons while between the plates.

a. Sketch a set of vectors showing the direction in which the electric field lines point between the plates.

b. Sketch a vector showing the direction in which the object will travel when placed between the plates.

4.1.4– Use equation to determine electric field strength; force; and/or charge. Map or recognize proper electric field maps for point charges or systems of charges. Explain the effect of charged parallel plates on electric field strength, electrostatic force, and acceleration of charges between such plates.

- A +2.0 coulomb charge experiences a force of 10 newtons while in an electric field. What is the strength of the electric field?

[5N/C] - What force will a 3.0 coulomb charge experience if place in an electric field

with a strength of 15 newtons per coulomb?

[45N] - What is the charge on an object that experiences a force of 20 newtons when it

is placed in an electric field with a strength of 4.0 newtons per coulomb?

[5C] + + + + + + + + + + + + + + + + + - - - - - - - - + + + + + + + + + + + + + + + + + - - - - - - - - - - -

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4.1.5 Electrical Potential (Voltage)

Electrical PE

• To increase PE

• To decrease PE

Calculating Potential Difference

– Amount of potential difference:

• ___________________________________________________

• ___________________________________________________ Equation

Example #1

• 6.0 joules of work are done in pushing an object with +3.0 coulombs of charge toward a charged plate.

– What type of charge does the plate have on it?

– How much potential energy was stored in the electric fields? – How much electrical potential was generated?

Example #2

+

-

+

- Sketch the electric field in the area around each point charge, set of point charges, and set of plates.

- Determine the direction of the electric field at the points selected in each picture.

[A;B ;C↓;D;E=0] - An proton is fired into the space between two parallel, oppositely charged

plates that produce an electric field of strength 2.0 x 10-11 newtons per coulomb.

o Sketch the path of the electron as it passes between the plates.

o Determine the amount of force exerted on the proton.

[3.2E-30N]

o Determine the acceleration of the proton.

[1.9E-3m/s2_]

– – – + + + + + + + + + + + + – – – – – – – – – – – – – – – + + – + + + + + + + + + + + + – – – – – – – – – – – – – – – A B C D E + + + + + + + + + + + + – – – – – – – – – – – – – – –

+

-

+

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• An object with a 2.0 coulomb charge is accelerated through a potential difference of 10 volts.

– How much kinetic energy does the object gain?

Electron-volts

• Alternate unit for work/energy:

– Raises 1e to an electrical potential of 1 V

– ___________________________________________________

• What is the energy needed to raise two electrons to a potential of 1.0 volt?

• What is the energy needed to raise four electrons to a potential of 2.5 volts?

Example #3

• An electron travels a distance of 2.0 x 10-3 meter as its electrical potential is raised by 300 volts.

– How much work is done on the electron?

PRACTICE

4) 45 joules of work are done in moving an object with a charge of -3.0 micro- coulombs toward a negatively charged plate.

a. Calculate the change in electrical potential (voltage) of the object after it is moved.

b. If the object were released, how much kinetic energy would it gain?

5) 5.0 electron-volts of energy are used to move two electrons through an electric field. Calculate the change in electrical potential (voltage) for these electrons.

4) In each case, determine if electrical potential is: increasing, decreasing, or not changing.

-

+

– – – – – – – – – – – – – – –

-

– – – – – – – – – – – – – – –

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- What is the amount of energy needed to move an electron through an electrical potential of 3.0 volts? Express this energy in both joules and electron-volts.

[3eV; 4.8E-19J] - An object with a 4.0 coulomb charge is accelerated through an electrical

potential of 12.0 volts. What amount of kinetic energy does the object gain? Express this energy in both joules and electron-volts.

[48J; 3E20eV]

4.1.5 – Explain how electrical potential relates to changes in distance between charged objects. Use equation to determine electrical potential, work/energy, and/or charge. Convert between joules and electron-volts.

- In which of the cases below is the electrical potential energy increasing? In which cases is the electrical potential energy decreasing? In which cases is the electrical potential energy remaining constant?

[A=inc; B=dec C=dec; D=dec; E=inc; F=const] - What is the electrical potential generated when 15.0 joules of work are done in

moving a 5.0 coulomb charge through an electric field?

[3V] - What is the amount of work needed to increase the electrical potential of a 2.0

coulomb charge by 8.0 volts?

[16J] - What is the charge on an object that requires 6.4 x 10-19 joules of work to be

moved through an electrical potential of 2.0 volts?

[3.2E-=19C or 2e]

+ + + –

+ + + + + + + +

– + -

+ + + + + + + + – – – – – – – – – – – – – – – –