Force of B on A ~ q A x q B

Static electricity

Source of electricity: Electric charges Everything (earth, you, the table etc) made of tiny particles called atoms Atoms are made up of 3 even tinier particles: Electrons, neutrons and protons The atom

Try this for a home experiment this weekend – yes I’m kidding Why does this person survive? Reminders: http://drmegavolt.com Lecture 20 : HW 8 due Today Reading for Tuesday: 10.3

Static electricity

Particle

Charge

Mass

Electron

-e

9.11×10-31 kg

Proton

+e

1.67×10-27 kg

Neutron

0

1.67×10-27 kg

e = 1.6 × 10-19 Coulombs Coulomb (C) is the unit of charge

Static electricity: What happens when charges are stationary Electricity (and electric currents): What happens when charges (usually electrons) are moving

Reading quiz

Reading quiz

1. Coulomb’s law describes a. The force between electrical point charges b. How dry your socks get in the dryer c. The friction force between items of clothing d. The operation of a conveyor belt

1. Coulomb’s law describes a. The force between electrical point charges b. How dry your socks get in the dryer c. The friction force between items of clothing d. The operation of a conveyor belt

2. Electric charges a. Can never move from one object to another b. Can never move inside an object c. Can move inside an object but not from one object to another d. Can move both inside an object and between objects, depending on what the objects are.

2. Electric charges a. Can never move from one object to another b. Can never move inside an object c. Can move inside an object but not from one object to another d. Can move both inside an object and between objects, depending on what the objects are.

3. An object that is electrically neutral a. Contains more positively charged particles (protons) than negatively charged ones (electrons) b. Contains more electrons than protons c. Contains no charged particles d. Contains equal numbers of protons and electrons. e. Is unable to conduct electricity

3. An object that is electrically neutral a. Contains more positively charged particles (protons) than negatively charged ones (electrons) b. Contains more electrons than protons c. Contains no charged particles d. Contains equal numbers of protons and electrons. e. Is unable to conduct electricity

Electrostatic force between charged particles

Sorting out how charges interact

opposite charges attract

like charges repel opposite charges attract

like charges repel

F

-

-

F

-

F

F

+

F

-

-

F

-

F

F

+

Consider 2 ‘point’ charges, A and B. What force does charge A feel?

What if I have twice the charge as before?

F

-

-

a) Half the force as before b) Same force as before c) Twice the force as before d) Four times the force

F

Twice the charges – twice the force Three times the charge, 3x the force Ten times the charge, 10x the force

qA

qB

Observed behavior: - Force depends on qA and qB : More charge, more force

Forceof B on A ~ qA x qB note: if q’s are the same sign, F is positive: pushing away if q’s are the opposite sign, F is negative: attracting together

1

Sorting out how charges interact opposite charges attract

like charges repel

F

-

Sorting out how charges interact

F

-

-

F

F

+

What about the distance, what if they are closer?

opposite charges attract

like charges repel

F

-

-

F

-

F

F

+

What about the distance, what if they are closer? Closer means more force!

-

F

-

F

F

-

-

F

What math relationship shows this?

Closer means more force! a) Less force b) Same force as before c) More force

a) Less force b) Same force as before c) More force

Putting this together: Electric Force F

-

A comment on units.

opposite charges attract

like charges repel

-

F

-

F

F

+

Consider 2 ‘point’ charges, A and B. What force does charge A feel?

r

qA

𝒒𝑨 𝒒𝑩 𝒓𝟐

qA

r

qB

𝑭𝒐𝒏 𝑩 𝒇𝒓𝒐𝒎 𝑨 = 𝒌

𝒒𝑨 𝒒𝑩 𝒓𝟐

• For discussion of units we use brackets: 𝑢𝑛𝑖𝑡𝑠 • To find the units on k→[?] we can use the fact that we need the thing on the right to have units 𝑁

qB

Observed behavior: - Force depends on qA and qB : More charge, more force - Force depends on distance between them (r) : less distance, more force

𝑭𝒐𝒏 𝑩 𝒇𝒓𝒐𝒎 𝑨 = 𝒌

F ~ 1/ r (is a good guess) But it turns out to be stronger ! F ~ 1 / r2

• Describes the force between 2 point charges • k is Coulomb constant = 9 x 109 N m2/C2 • qA and qB are amount of charge in coulombs (C ) • r is separation in m 1 Coulomb = 6 x 1018 electron charges!

• So 𝑁 = ?

𝐶2 𝑚2

• This means that ? = [ 𝑁

𝑚2 𝐶2

]

Units are a good way to make sure you’ve done your algebra correctly. BUT they are difficult to carry around.

An electron and a proton are 1 mm apart

B proton

A electron

-

0.001 m

What is force between them? Calculate and write down answer.

+

𝑭𝒐𝒏 𝑩 𝒇𝒓𝒐𝒎 𝑨 = 𝒌

𝒒𝑨 𝒒𝑩 𝒓𝟐

B proton

A electron

-

0.001 m

What is force between them? Calculate and write down answer.

+

k is Coulomb constant = 9 x 109 N m2/C2 e = 1.6 x 10-19C

Force between particles = -2.3 x 10-22 N

Proton and electron have charges of same magnitude (e) , opposite sign  qA = - 1.6 x 10-19 C qB = + 1.6 x 10-19 C

a) Force on electron points to left

𝑭𝒐𝒏 𝑩 𝒇𝒓𝒐𝒎 𝑨 = 𝒌

𝒒𝑨 𝒒𝑩 𝒓𝟐

What does the minus sign mean? b) Force on electron points to right

𝑵𝒎𝟐 −𝟏. 𝟔 × 𝟏𝟎−𝟏𝟗 𝑪 𝟏. 𝟔 × 𝟏𝟎−𝟏𝟗 𝑪 ) 𝑪𝟐 𝟏 × 𝟏𝟎−𝟑 𝒎 𝟐 𝟏𝟎𝟗−𝟏𝟗−𝟏𝟗 𝑭 = 𝟗 × −𝟏. 𝟔 × 𝟏. 𝟔 𝑵 = −𝟐𝟑. 𝟒 × 𝟏𝟎−𝟐𝟗+𝟔 𝑵 𝟏𝟎−𝟔 𝑭 = (𝟗 × 𝟏𝟎𝟗

𝑭 = −𝟐. 𝟑 × 𝟏𝟎−𝟐𝟐

2

B proton

A electron

-

0.001 m

What is force between them? Calculate and write down answer.

+

𝑭𝒐𝒏 𝑩 𝒇𝒓𝒐𝒎 𝑨 = 𝒌

𝒒𝑨 𝒒𝑩 𝒓𝟐

Balloon demo: Rub a balloon on sweater and stick it to the wall. What attracts the balloon to the wall? After I have rubbed the balloon on my sweater, predict what charges will be on the balloon and on sweater a. b. c. d. e.

so Force = -2.3 x 10-22 N What does the minus sign mean? b) Force on electron points to right Remember force is a vector and so requires both a magnitude and direction  Plugging numbers into Coulomb’s Law give the magnitude of the force  What about the direction?

Both have extra + charges. Both have extra - charges Balloon has extra + or - charges, sweater neutral, Sweater has extra + or - charges, balloon neutral Either sweater has extra - and balloon extra + or balloon extra – and sweater extra +.

Look at Phet and find out……..

The force between 2 point charges always acts ‘along the line of centers’ Answer is e:

- If Coulomb’s law gives a positive number, the charges repel - If Coulomb’s law gives a negative number the charges attract

Alternatively: Use Coulomb’s law to find the magnitude of the force Look at diagram to find direction

Remember atoms are initially neutral Electrons in sweater atoms are bound to atom less strongly than in balloon atoms Rubbing allows balloon atoms to steal electrons, making balloon negatively charged (excess of electrons) and sweater positively charged

Rub a second balloon on the sweater. The two balloons will .. a. attract, b. repel, c. not exert a force on each other

Balloon Sim

b. repel: • Balloons made of same material so must pick up same sign of charge from sweater • Like charges repel

Move charged balloon close to wall. What will happen? a. Wall is neutral (no extra + or -) so will not be affected. b. - charges in wall will move away, + towards balloon c. + charges in wall will move away, - towards balloon. d. - charges in wall will move away, + don’t move.

http://phet.colorado.edu/en/simulation/balloons

Electrostatic dust rag (think SwifferTM). Rub it on surface, it’s very good at attracting electrons and so becomes negatively charged.

Rub a second balloon on the sweater. The two balloons will .. a. attract, b. repel, c. not exert a force on each other b. repel: • Balloons made of same material so must pick up same sign of charge from sweater • Like charges repel

Move charged balloon close to wall. What will happen? d. - charges in wall will move away, + don’t move. . • Negative charge on balloon repels –charge and attracted to + charge in the wall • Atoms in wall become stretched (or polarized) Remember force between charges = 𝒌

𝒒𝑨 𝒒𝑩 𝒓𝟐

+ normal

+ polarized

• Balloon is closer to + charges in wall than – charges, so force of attraction is stronger than force of repulsion

What kind of dust will this negatively charged rag pick up best?

-

+ +

-

a. b. c. d.

Only dust with positive charges. Only dust with negative charges. The rag will pick up all dust equally. The rag will pick up dust with positive charges, and also neutral dust particles, just not as well. e. The rag will pick up dust with negative charges, and also neutral dust particles, just not as well.

3

Van de Graaff generator.

Electrostatic dust rag (think SwifferTM). Rub it on surface, it’s very good at attracting electrons and so becomes negatively charged.

-

What kind of dust will this negatively charged rag pick up best?

-

+

+

-

This “generator” collects charges on the large sphere.

a. b. c. d.

Only dust with positive charges. Only dust with negative charges. The rag will pick up all dust equally. The rag will pick up dust with positive charges, and also neutral dust particles, just not as well. e. The rag will pick up dust with negative charges, and also neutral dust particles, just not as well.

- - -

-

-

-

-

It does this by repeatedly rubbing “balloons” on a “sweater” and transferring the excess electrons up to the top of the support post

-

-

--

The “balloon” is a rubber belt that is circulated by a motor A brush similar to a sweater gives the belt electrons A different brush (that really likes electrons) us used at the top to pull off the electrons and charge up the generator

Van de Graaff generator. If I bring a pom-pom up to the generator and touch it what will happen?

Bring uncharged metalized mylar balloon up to Van de Graaff. -

-

-

-

-

-

a) Nothing. The electrons won’t go anywhere. b) The electrons will charge up the pom-pom but you won’t be able to see anything c) The electrons will charge up the pom-pom and then the strands will repel each other. d) I don’t know

Predict what will happen:

- - -

1. Before it touches 2. After it touches

1. Before touching a. Not affected by VdG b. Attracted to it c. Repelled

-

-

- - -

-

-

-

-

-

-

-

-

2. After touching a. Not affected by VdG b. Attracted to it c. Repelled

Bring uncharged metalized mylar balloon up to Vandergraff.

Bring uncharged metalized mylar balloon up to Vandergraff.

Predict what will happen:

Predict what will happen:

1. Before it touches 2. After it touches

- +

1. Before touching a. Not affected by VdG b. Attracted to it c. Repelled

- - -

1. Before it touches 2. After it touches

-

-

-

-

-

-

• Charges in neutral ball are polarized by – charge on VdG • + charges move closer to VdG, - charges move away • Force between charges = kqAqB r2

-

-

2. After touching a. Not affected by VdG b. Attracted to it c. Repelled

---

- - -

-

-

-

-

-

-

-

-

• When balloon touches, - charges are pushed onto it by the other – charges on the VdG • Now balloon is negatively charged like VdG • Like charges repel

• + charges on ball are closer to VdG, so force of attraction is strongest

4

Discussion of Energy

Mechanical work vs. Electrical

• 3 Types of energy (there are others):

Kinetic - energy of motion - rock rolling down hill Potential - ability to do work in future - rock at the top of a hill or a fluid has it under pressure. Thermal - energy that dissipates as heat (e.g. friction, or smashing into a wall)

Think, climbing up a hill stores energy in system Same thing, separating charges…

• How would this apply to charges? +

-

-

• Think of the analogy of a hill… pulling + away from valley…

Hill Analogy for energy Effort (push) to get ball (at constant speed):

up the hill

a) harder at first b) easier at first

F

F

+

We just have to be more careful because unlike mass (all masses attract each other) some charges attract while others repel

Hill Analogy for energy Potential Energy of same ball

a

a) PEa > PEb b

b) PEb > PEa c) PEa = PEb

c) takes same effort / push

The force required is related to the steepness or slope of the potential energy curve. Steeper means more force.

Hill Analogy for energy

Voltage

Energy of ball (Potential Energy, PE)

a)

a) PEa > PEb b)

b) PEb < PEa c) PEa = PEb

Gravitational PE = mgh Notice: it takes less force to go up further at a) but it has more potential energy. Force is steepness not magnitude of potential energy

http://phet.colorado.edu/sims/charges-and-fields/charges-and-fields_en.html

5

Voltage has to do with conditions of system • Amount of charge • Distance from that charge • Like the electric force (related but different)

Topo- practice • Which figure goes with #4

Voltage is like the height of mountain

• Think Topographical maps

Voltage tells you what a + charge will do

+5V

-5V

+V is like top of hill -V Is like valley 0V

• Answer C Where is 0 V?

What will a +q do at 0V: a) Be attracted to higher voltage b) Be attracted to lower voltage c) Not be impacted b) Just like a ball rolls down hill

Voltage is like the height of mountain

• Height (and gravity) • Voltage • Mass, m • Charge, q • Electrical Potential Energy • Gravitational potential Energy EPE = q D V

GPE = m g Dh

Electrostatic potential energy and voltage New force: Electrostatic force between charges New PE: Electric Potential Energy (EPE) Forces and PE go in pairs - Remember gravitational force: - Do work against gravitational force (mg) to raise an object’s GPE (mgh) - Similarly, do work against electric force to raise an object’s EPE EPE = q DV, where q = charge of object and DV is voltage difference Like GPE with q  m and DV  gDh Voltage (V) - tells you EPE of any charge at that location in space - Tells you work required to bring a unit charge from V = 0 to that location - Determined by surrounding charges. Closer you are to + charge the more + the voltage - A grounded object is always at V = 0. Grounded means attached to the ground! - Always interested in DV: voltage difference between 2 locations like GPE where only Dh mattered Best understood by doing practice questions!

6

Two metal plates connected by a battery. Battery maintains a voltage difference of V between the plates

Conservation of energy and EPE Remember conservation of energy equation:

A -

Work Done on object = Change in Energy of object Wext - Wfriction = DPE + DKE

-

Now we can add another PE term to this equation:

a) b) c) d)

Two metal plates connected by a battery. Battery maintains a voltage difference of V between the plates

-

V

V

0 +V -V - determine from information given Can’t

q

A

++

-

B

++

-

q + + + + + +

B

Plate A-is grounded (set to zero V) What is the voltage of plate B?

Wext - Wfriction = DGPE + DEPE + DKE = mgDh + qDV + D(1/2mv2)

A

q + + + + + +

++

-

V

+ + + + + +

B

What will happen to the charge q if we let go of it (ignore gravity)? a) Nothing b) It will fly over to plate A c) Sparks will fly d) -Something else

Plate A-is grounded (set to zero V) What is the voltage of plate B? a) b) c) d)

0 +V -V - determine from information given Can’t

Note: Conductors (bits of metal, wires etc) are a constant voltage all over

q

A

++

-

V

+ + + + + +

B

q

A

++

-

-

V

+ + + + + +

B EPE = qDV

-

What will happen to the charge q if we let go of it (ignore gravity)?

What is the change in EPE of charge as it flies from plate B to plate A?

a) Nothing b) It will fly over to plate A c) Sparks will fly d) -Something else

a) b) c) d)

0 +qV -qV Can’t determine -

q has a + charge. It will be repelled by + charges on plates B and attracted to - charges on plate A

7

q

A

+ + + + + +

++

-

V

B

q

A -

EPE = qDV

-

-

B

+ + + + + +

++

V

Conservation of energy: Wext - Wfriction= DGPE + DEPE + DKE

-

What is the change in EPE as charge flies from plate B to plate A? c) -qV

Charged particle loses EPE as it flies from B to A. What form has this energy turned into just before it hits plate A

At B: EPE = q V At A: EPE = q × 0 = 0

a) b) c) d)

-

Change in -EPE = EPEf – EPEi = 0 – qV = -qV

-

KE Thermal energy GPEPPE

Plug in numbers: q = +2e = 2×1.6×10-19C = 3.2×10-19C V = 100 V DEPE = - 3.2×10-17J

CT 29.4b

q

A -

+ + + + + +

++

V

-

B Conservation of energy: Wext - Wfriction= DGPE + DEPE + DKE

Charged particle loses EPE as it flies from B to A. What form has this energy turned into just before it hits plate A a) b) c) d)

-

A positive charge q is released from position i to position f between the charged plates. Did the electric potential energy (PE) increase or decrease? Did the voltage (V) at the position of the test charge increase or decrease? A: PE , V C: PE , V E: None of these.

B: PE , V D: PE , V

KE Thermal energy GPEPPE

Just before it hits plate: qV = 1/2mv2 Just after it hits plate, all this energy has turned into thermal energy ©University of Colorado, Boulder (2008)

CT 29.4b

A positive charge q is released from position i to position f between the charged plates. Did the electric potential energy (PE) increase or decrease? Did the voltage (V) at the position of the test charge increase or decrease? A: PE , V C: PE , V E: None of these.

B: PE , V D: PE , V

CT 29.4

A negative charge -q is released from position i to position f between the charged plates of a charged capacitor. Did the potential energy (PE) increase or decrease? Did the voltage (V) at the position of the test charge increase or decrease? A: PE , V B: PE , V C: PE , V D: PE , V E: None of these. Hint: EPE = qDV

©University of Colorado, Boulder (2008)

©University of Colorado, Boulder (2008)

8

CT 29.4

A negative charge -q is released from position i to position f between the charged plates as shown.

Electrostatics Summary

Did the potential energy (PE) increase or decrease? Did the voltage (V) at the position of the test charge increase or decrease?

• Positive and negative charge: Like charges repel, opposites attract • Coulombs law for point charges: F = k qA qB r2 Force acts along line joining particles

A: PE , V B: PE , V C: PE , V D: PE , V E: None of these.

• Voltage: Determines EPE of charge at that location in space Close to + charges voltage is more + and vice versa Grounded object is at 0V

EPE = qDV Vf > Vi DV is bigger! EPE is qDV but q is negative EPE gets smaller!

(Also called Electric Potential) • EPE: = qDV New form of potential energy Lots of analogies to GPE (DVDh, qm) ©University of Colorado, Boulder (2008)

Flashlights, circuits, batteries, and power light bulb circuit

+

+

• Start by looking at a really simple circuit containing - light bulb - Battery - Wires • Each element made of metal containing electrons that are free to move

=

• Given batteries, light bulbs, and wire, how can we design a light bulb circuit a) that will burn brightest, b) that will last longer, c) that will be dim, d) that will turn on and off. • How can you control and predict current and power in light bulbs? • All this basic circuit stuff applies to home wiring, home electronics, heaters etc. • Thursday lecture … help save lives … physics of dangers of electrocution.

• What are the electrons doing in each element to ensure that the light bulb lights up?

Builds on electrostatics (like charges repel, opposite charges attract, voltage, EPE) ………but now electrons are moving…………………

+

Using each of these three elements can you draw a picture where the bulb lights up?

………. need to start thinking like an electron!

light bulb circuit: Wiring

light bulb circuit: Wiring + +

What will happen when hook up positive end of battery (+) to flashlight bulb with one wire? b. barely light up

c. not light up

+

a. light up

+ +

What will happen when hook up positive end of battery (+) to flashlight bulb with one wire? a. light up b. barely light up c. not light up

+

+ -

+ ++ ++

+ +

-

• Light requires steady flow of electrons through bulb • But nowhere for electrons to flow!!! - Electrons in wire initially attracted to positive end of battery - This makes wire and filament positive - Electron flow stops when attractions to + end of battery and positively charged wire are equal. (technically they are at the same voltage!)

9

See this in action!

http://phet.colorado.edu/en/simulation/circuit-construction-kit-dc

10