ElectrostaticElectrostaticss

Electric Charges Electric Charges : the basis of : the basis of electricity is charge.electricity is charge.

- The charge on an - The charge on an atom is determined by atom is determined by the subatomic particles the subatomic particles that make it up.that make it up.

Proton- has a positive charge and is located in the nucleus.Neutron- has no charge (is neutral) and is also located in the nucleus as it fills in the spaces between the protons.Electron- has a negative charge and is located outside of the nucleus in an electron cloud around the atom.

Particle charges:Particle charges:- Electrons and protons have the same magnitude of charge- Electron (-e): -1.60 x 10-19 C- Proton (+e): +1.60 x 10-19 C- This is why electrons are forced to orbit around the nucleus.- Electrostatic Forces hold atoms together.- The Law of Charges- Like charges repel, and unlike charges attract.

Subatomic Particle SizesSubatomic Particle Sizes A proton and neutron have about the same mass - A proton and neutron have about the same mass - 1.67 x 101.67 x 10-27-27 kg kg An electron has a much smaller mass - An electron has a much smaller mass - 9.11 x 109.11 x 10-31-31 kg kg

To put this into perspective it’s like comparing the sizes of a penny and large bowling ball. The proton is obviously the bowling ball and the electron is represented by the penny.

How do atoms become How do atoms become “charged ?”“charged ?”- Atoms become charged when they - Atoms become charged when they become more positive or more negative.become more positive or more negative.- How can this happen?- How can this happen?

- Remove or add a proton or an electron. - Protons and neutrons are bound together by the Strong Nuclear Force and it is very hard to separate them.

- Electrons, however, can be more easily removed.

IonsIons

An atom with a deficiency of electrons is positively charged.

An atom with an excess of electrons is negatively charged.

ATOMS DO NOT GAIN OR LOSE PROTONS!!!!

Charge is a fundamental quality Charge is a fundamental quality like mass.like mass.- Charge is denoted as q.- Charge has a fundamental unit of a Coulomb (C).- Charges are usually really really small numbers (10-).- So what is 1 C?

An object would have to have 6.25 x 1018 extra electrons to amount to –1 C of charge.A lightning bolt is estimated to carry a charge of 10 C.

- Revisit the charges on an electron and proton.

Charges can ONLY be in multiples of Charges can ONLY be in multiples of eeRemember:

• -e = an electron = -1.60 x 10-19 C• +e = a proton = +1.60 x 10-19 C

An object that has a net charge of 8.0 x 10-19 C has a net charge of what multiple of e? Hint: How many electrons would need to be removed to create this charge?

The net charge would be +5e, 5 electrons were removed

Multiples of Charges ChartMultiples of Charges Chart

1e 1.6 x 10-19

2e 3.2 x 10-19

3e 4.8 x 10-19

4e 6.4 x 10-19

5e 8.0 x 10-19

Electrostatic ForceElectrostatic Force- This is a non-contact force (like the gravitational force except instead of two masses exerting force on each other the two objects charges exert a force of repulsion or attraction).- ANY charged object can exert the electrostatic force upon other objects- both charged and uncharged objects.

Coulomb’s Law - Coulomb’s Law - formula formula for electrostatic forcefor electrostatic force

Again this is similar to the gravitational force…

Fg = GmM

r2charge (q) is now

responsible for the force

Fe = kq1q2

r2

Just like G was a constant so is Just like G was a constant so is k. k. k is the k is the electrostatic constant and = and = 8.99 x 109 N•m2/C2

Remember this…the relationship between the gravitational force and the distance from the object…this is the inverse square law

2x 3x 4x

1/4 = 2.24 1/9 = 1.09 1/16 = 0.61

1x

9.81 m/s2

FFgg

rr22

Fg = GmM

r2

Fe = kq1q2

r2

FFee

rr22

Try this…Try this…The distance between a proton and an electron in a hydrogen atom is 5.3 x 10-11 m. Find both the gravitational force and the electrostatic force between the two particles.

ANY charged object, whether ANY charged object, whether positively charged or positively charged or negatively charged, will have negatively charged, will have an ATTRACTIVE interaction an ATTRACTIVE interaction with a neutral object.with a neutral object.

A balloon when rubbed on your head becomes charged by picking up extra electrons from your hair.

That same balloon, because it is charged, will attract a neutral object like pieces of paper.

-+

-

So we are able to predict the So we are able to predict the charge on objects based on charge on objects based on their interaction with other their interaction with other objects.objects.

They can either They can either both be positive or both be positive or both be negative.both be negative.

They can have They can have opposite charges opposite charges or one object is or one object is charged and the charged and the other is neutral.other is neutral.

Try this…Try this…- On two occasions, the following charge interactions between balloons A, B and C are observed. In each case, it is known that balloon B is charged negatively. Based on these observations, what can you conclude about the charge on balloon A and C for each situation.

positive or neutral

positive

positive (if it was neutral it wouldn’t repel C)

positive

Why does the balloon stick to Why does the balloon stick to the wall?the wall?

- When a balloon is rubbed with a piece of cloth electrons are transferred between the two objects. Usually the balloon attracts extra electrons and then receives an overall negative charge.

When the balloon is placed against the wall the excess electrons will repel the electrons in the wall and be attracted to the positive charges.

What happens to your hair when you What happens to your hair when you rub a balloon on your head ?rub a balloon on your head ?

• The balloon, after being rubbed and then pulled away, removes some of the electrons in your hair which give each strand a positive charge. Like charges want to repel and each strand is repelling from the others and “sticking up.”

Getting ShockedGetting Shocked

- As you walk across a carpet, electrons are transferred from the rug to you. - Now you have extra electrons. - Touch a door knob (conductor) and ZAP! - The electrons move from you to the knob.

LightningLightning- Lightning is a REALLY - Lightning is a REALLY big shock.big shock.- Positive charges tend - Positive charges tend to go up, negative to go up, negative charges tend to go charges tend to go down. down. - When the attraction - When the attraction reaches a critical level reaches a critical level you get a lightning you get a lightning bolt.bolt.

Objects that tend to Objects that tend to give up give up electronselectrons and become and become positivepositive : :

- Glass- Glass- Nylon- Nylon- Fur- Fur- Hair- Hair- Wool- Wool

Objects that tend to Objects that tend to attract attract electrons electrons and become and become negativenegative : :

- Rubber- Rubber- - PolyesterPolyester- - StyrofoaStyrofoamm- Saran - Saran WrapWrap- PVC- PVC

Insulators and ConductorsInsulators and Conductors- Different materials hold electrons - Different materials hold electrons differently.differently.- Insulators- Insulators don’t let electrons move don’t let electrons move around within the material freely.around within the material freely.

Ex. Cloth, Plastic, Glass, Dry Air, Wood, Ex. Cloth, Plastic, Glass, Dry Air, Wood, RubberRubber

- Conductors- Conductors do let electrons move do let electrons move around within the material freely.around within the material freely.

Ex. Metals- Silver, Copper, AluminumEx. Metals- Silver, Copper, Aluminum

Try this…Try this…

• A charged plastic rod is brought A charged plastic rod is brought close a neutral metal sphere. How close a neutral metal sphere. How would the distribution of charges be would the distribution of charges be in the metal sphere?in the metal sphere?

Try this…Try this…• Which of the diagrams below best represents the charge Which of the diagrams below best represents the charge

distribution on a metal sphere when a positively charged distribution on a metal sphere when a positively charged plastic tube is placed nearby?plastic tube is placed nearby?

Law of Conservation of Law of Conservation of ChargeCharge• Charges within a closed system may be transferred from one Charges within a closed system may be transferred from one

object to another, but charge is neither created nor destroyed.object to another, but charge is neither created nor destroyed.

The diagram below shows the initial charges and positions of The diagram below shows the initial charges and positions of three metal spheres, R, S, and T, on insulating stands.three metal spheres, R, S, and T, on insulating stands.

0e -8e +6e

R S T

Sphere R is brought into contact with sphere S and then removed. Sphere R is brought into contact with sphere S and then removed. Then Then

sphere S is brought into contact with sphere T and removed. sphere S is brought into contact with sphere T and removed. What is the charge on sphere T after this procedure is completed ? What is the charge on sphere T after this procedure is completed ?

Note that the net

charge of the

system is -2e.

0e -8e

R S

When the spheres come in contact the charge will be When the spheres come in contact the charge will be

distributed evenly between both spheres.distributed evenly between both spheres.

-4e -4e +6e

T

0e -8e

S T

-4e +6e-4e

R

-4-4ee + 6 + 6e e ==

22

+2+2e e ==

22

++ee

+e +e

Note : that the charge of the system is conserved Note : that the charge of the system is conserved - the initial charge is the same as the final charge. - the initial charge is the same as the final charge.

-4e +e +e

R S T

-4-4ee + + ee + + ee = -2 = -2ee

Electroscopes - instruments Electroscopes - instruments used to detect chargeused to detect charge

The yellow arms or leaves on both instruments will The yellow arms or leaves on both instruments will

move to show the charge.move to show the charge.

Charged Electroscope

Excess of the same charge in both leaves Excess of the same charge in both leaves

causes them to diverge/repelcauses them to diverge/repel

+ +-+-

+-+ ++-+

Uncharged Electroscope

Leaves are neutral so they are not Leaves are neutral so they are not

diverging/repelling or converging/attracting.diverging/repelling or converging/attracting.

+-

+- +-

+-+- +-

Steps in charging an electroscope by Steps in charging an electroscope by INDUCTIONINDUCTION ::

1. Uncharged electroscope: 1. Uncharged electroscope:

+-+-+-

+-+-+-

+-+-+-

Leaves are just Leaves are just

hanging straight down.hanging straight down.

Net charge is zero.Net charge is zero.

2. A negatively charged rod is brought near the electroscope: 2. A negatively charged rod is brought near the electroscope:

++++

+-+-+-

+-+-+-

-- -- --- ----- -- ---- -- --- -- ----- - -

--- Net charge is zeroNet charge is zero

-- -- --- -- ----- ---- -- --- -- ----- -

3. Electrons move to the leaves: 3. Electrons move to the leaves:

++++

+- +- +-

-+-+-+

Net charge is still zeroNet charge is still zero

----

-- -- --- -- ----- ---- -- --- -- ----- -

4. Leaves diverge: 4. Leaves diverge:

++++

+--+--+-

-+-+-

-+-

Net charge of zeroNet charge of zero

+--+--+-

-+-+--+-

-- -- --- -- ----- ---- -- --- -- ----- -

5. The electroscope is grounded: 5. The electroscope is grounded:

++++

+--+--+-

-+-+-

-+-

GroundingGrounding is the is the

process of process of removingremoving

the excess charge on the excess charge on

an object by means an object by means

of the transfer of of the transfer of

electrons between it electrons between it

and another object and another object

of substantial size.of substantial size.

-- -- --- -- ----- ---- -- --- -- ----- -

6. Electrons go to the ground: 6. Electrons go to the ground:

++++

+-+-

+-

-+-+

-+-- -- Net charge is Net charge is

now positivenow positive

-- -- --- -- ----- ---- -- --- -- ----- -

7. Leaves converge and ground is removed: 7. Leaves converge and ground is removed:

++++

+-+-+-

-+-+-+

+-+-

+-

-+-+

-+

-- -- --- -- ----- ---- -- --- -- ----- - +

+++

+-+-+-

-+-+-+

8. Negatively charged rod is removed: 8. Negatively charged rod is removed:

++++

++-+-

+-+-+

9. Electrons redistribute throughout the electroscope and 9. Electrons redistribute throughout the electroscope and

move up toward the top: move up toward the top:

--

++++

++-+-

+-+-+

--

10. Leaves now have the same charge and diverge: 10. Leaves now have the same charge and diverge:

++-

+-

+-+

-+

Field Near a Negative Field Near a Negative ChargeCharge

Note that the field Note that the field EE in the vicinity of a in the vicinity of a negative negative chargecharge –Q –Q is is toward toward the charge—the direction that a the charge—the direction that a +q+q test charge would move. test charge would move.

Force on Force on +q+q is with is with field direction.field direction.

Force on Force on -q-q is is against field against field

direction.direction.

E

Electric Field

.r

++qF

---- - ----Q

E

Electric Field

.r

--qF

---- - ----Q

The Magnitude of E-FieldThe Magnitude of E-FieldThe The magnitudemagnitude of the electric field intensity at a of the electric field intensity at a point in space is defined as the point in space is defined as the force per unit force per unit chargecharge (N/C)(N/C) that would be experienced by any that would be experienced by any test charge placed at that point.test charge placed at that point.

Electric Field Intensity E

N; Units C

FEq

The The directiondirection of of EE at a point is the same as the at a point is the same as the direction that a direction that a positivepositive charge would move charge would move IFIF placed at that point.placed at that point.

++++ +

+++Q

.r P

The E-Field at a distance r The E-Field at a distance r from a single charge Qfrom a single charge Q

++++ + +++Q

.r P

Consider a test charge Consider a test charge +q+q placed placed at at PP a distance a distance rr from from QQ..

The outward force on +q is:The outward force on +q is:

The electric field The electric field EE is therefore: is therefore:2F kQq rE

q q 2

kQEr

++qF

2

kQqFr

E

2

kQEr

The Resultant Electric The Resultant Electric Field.Field.

The resultant field The resultant field EE in the vicinity of a number in the vicinity of a number of point charges is equal to the of point charges is equal to the vector sumvector sum of the of the fields due to each charge taken individually.fields due to each charge taken individually.

Consider E for each charge.Consider E for each charge.

+

- q1

q2q3 -

AE1

E3

E2

ER Vector Sum:

E = E1 + E2 + E3

Directions are based on positive test charge.

Magnitudes are from:

2

kQEr

Electric Field LinesElectric Field Lines

++++ + +++Q --

-- - ----Q

Electric Field LinesElectric Field Lines are imaginary lines drawn in are imaginary lines drawn in such a way that their direction at any point is the such a way that their direction at any point is the same as the direction of the field at that point.same as the direction of the field at that point.

Field lines go Field lines go awayaway from from positivepositive charges and charges and towardtoward negativenegative charges. charges.

1. The direction of the field line at any point is 1. The direction of the field line at any point is the same as motion of +q at that point.the same as motion of +q at that point.

2. The spacing of the lines must be such that they 2. The spacing of the lines must be such that they are close together where the field is strong and are close together where the field is strong and far apart where the field is weak.far apart where the field is weak.

+ -qq11 qq22

EE11

EE22

EERR

Rules for Drawing Field LinesRules for Drawing Field Lines

Examples of E-Field LinesExamples of E-Field LinesTwo equal but Two equal but oppositeopposite charges. charges.

Two Two identical identical charges (both +).charges (both +).

Notice that lines Notice that lines leave +leave + charges and charges and enterenter - - charges.charges.Also, Also, EE is is strongeststrongest where field lines are where field lines are most densemost dense..

Summary of FormulasSummary of FormulasThe Electric Field Intensity E: 2

N Units are C

F kQEq r

The Electric Field Near several charges: 2 Vector SumkQE

r

Work to Move a ChargeWork to Move a ChargeWork to move +q from Ato B.

++++ + +++Q

qE

F

ra

rb2a

a

kqQFr

avga b

kqQFr r

At A:

At B:

Avg. Force:

2bb

kqQFr

Distance: ra - rb

( )a ba b

kQqWork Fd r rr r

1 1

b a

Work kQqr r

Absolute Potential EnergyAbsolute Potential Energy

++++ + +++Q

qE

F

ra

rb

1 1

b a

Work kQqr r

Absolute P.E. is Absolute P.E. is relative to relative to

It is work to bring It is work to bring +q+q from infinity to from infinity to point near point near QQ—i.e., —i.e., from from to rto rbb

1 1

b b

kQqWork kQqr r

Absolute Potential Energy:

kQqUr

0

Properties of SpaceProperties of SpaceAn electric field is a property of space allowing prediction of the force on a charge at that point.

; FE F qEq

The field E exist independently of the charge q and is found from:

2 : kQElectric Field Er

E

Electric Field

++++ + +++Q

r

E is a Vector

Electric PotentialElectric Potential

Potential++++ + +++Q

.r

Electric potentialElectric potential is another property of is another property of space allowing us to predict the P.E. of space allowing us to predict the P.E. of anyany charge q at a point. charge q at a point.

UVq

; UV U qVq

Electric Electric Potential:Potential:

The units are: joules per coulombjoules per coulomb (J/C)(J/C)

For example, if the potential is For example, if the potential is 400 J/C400 J/C at point at point PP, , a a –2 nC–2 nC charge at that point would have P.E. : charge at that point would have P.E. :

U = qV = (-2 x 10-9C)(400 J/C); U = -800 nJ

P

The SI Unit of Potential The SI Unit of Potential (Volt)(Volt)

From the definition of electric potential as From the definition of electric potential as P.E. per P.E. per unit chargeunit charge, we see that the unit must be , we see that the unit must be J/CJ/C. We . We redefine this unit as the redefine this unit as the volt (V).volt (V).

1 joule; 1 volt = 1 coulomb

UVq

A potential of one volt at a given point means that a charge of one coulomb placed at that point will experience a potential energy of one joule.

Calculating Electric Calculating Electric PotentialPotential

Potential++++ + +++Q

.r

kQVr

PElectric Potential Energy and Electric Potential Energy and Potential:Potential:

; kQq UU Vr q

Substituting for Substituting for U, we find V:U, we find V:

kQqr kQV

q r

kQVr

The potential due to a positive charge is positive; The potential due to a negative charge is positive. (Use sign of charge.)

Potential DifferencePotential DifferenceThe potential difference between two points A and B is the work per unit positive charge done by electric forces in moving a small test charge from the point of higher potential to the point of lower potential.

Potential Difference: VAB = VA - VB

WorkAB = q(VA – VB) Work BY E-field

The positive and negative signs of the charges may be used mathematically to give appropriate signs.

Parallel PlatesParallel PlatesVA + + + +

- - - -VB

E+q

F = qE

Consider Two parallel plates of equal Consider Two parallel plates of equal and opposite charge, a distance and opposite charge, a distance dd apart.apart.

Constant E field: F = qE

Work = Work = FdFd = (qE)d= (qE)d

Also, Work = Also, Work = q(Vq(VAA – V – VBB))

So that: So that: qV qVAB AB = qEd = qEd andand VAB = Ed

The potential difference between two oppositely charged parallel plates is the product of E and d.

Summary of FormulasSummary of Formulas; kQq UU V

r q

kQVr

WorkAB = q(VA – VB) Work BY E-field

; VV Ed Ed

Electric Potential Energy and Potential

Electric Potential Near Multiple charges:

Oppositely Charged Parallel Plates:

The endThe end

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