Electrostatics

Chapter 32

Chapter 33

Five Topic Areas

• There are five main topic areas in physics:

• Mechanics

• Heat and Thermodynamics

• Electricity and Magnetism

• Waves, Sound, Light

• Atomic and Nuclear Physics

• We are now starting Electricity and Magnetism (E&M)

• For some, this is a difficult topic area ~ mainly because it involves particles that are too small to see

• What chapters are part of this unit? See next slide …

E&M Chapter Titles:

• Electrostatics: the study of charges at rest

• Circuits: the study of charges in motion

• Magnetism: the study of the effects of moving charges in a stationary magnetic field

• Induction: the study of how changing a magnetic field can be used to induce the movement of charges (create electricity)

Electrostatics

• Electrostatics: the study of charges at rest

• Static electricity

• Electric force

• Electric field

• Electric potential

Imtroducing Charge . . .

• There are four conservation laws in physics: • Conservation of mass

• Conservation of energy

• Conservation of momentum

• Conservation of charge

• Law of Conservation of Charge: charge cannot be created or destroyed

• Charge is created by the transfer of electrons

• If an object has extra electrons, it is negatively charged

• If an object is missing electrons, it has a positive charge

• Electrons are most easily transferred by friction or by rubbing. Think of scuffing your feet on the carpet.

Ex: Charging by Friction . . .

• Some materials give up electrons more readily than others. Rabbit fur readily gives up electrons.

Facts about Charge:

• Variable for charge: Q or q

• Unit of charge: Coulombs, C (named after Mr. Coulomb)

• Charge can be positive or negative: +Q and –Q

• An electron is often written as -q or e-

• Charge of electron/proton: • Charge of 1 electron, -q = -1.6 x 10-19 C

• Charge of 1 proton, +q = +1.6 x 10-19 C

• Definition of Coulomb:

• 1 C = charge accumulated by 6.25 x 1018 electrons, very dangerous!!

Charge is Quantized . . .

• Charge can only be transferred in whole number multiples of electrons. That is, you cannot transfer half an electron.

• This means that charge in “quantized.”

• Quantized: only exists in discrete amounts

• Money is also quantized. You cannot transfer less than 1 cent.

• All values of charge are multiples of 1.6x10-19 C

• Object gains 1 electron: q = 2(-1.6x10-19 C)

• Object gains 200 electrons: q = 200(-1.6x10-19 C)

• 5000 electrons are lost: q = 5000(+1.6x10-19 C)

Quantized: More examples . . .

• Quantized means “only exists in discrete amounts.”

• Comes from the word quantum that means the smallest amount of something

• Quantum of bag of marbles: 1 marble

• Quantum of box of crayons: 1 crayons

• Quantum of US money: 1 cent

• Quantum of charge: 1.6 x 10-19 C

• Quantum of negative charge = electron

• Quantum of positive charge = proton

• Ramp vs staircase analogy:

On a ramp, the crate can be anywhere.

The location is un-quantized.

On a staircase, the crate can only exist at

certain heights. The height is quantized.

Static Charge Examples

Static Electricity

• Section 16.1-16.4:

• Electroscope: an instrument used to detect the presence of an electrostatic charge

• Charging by conduction vs charging by induction

Free body diagrams . . .

Sketch fbd of each pith ball

Electric Force

Chapter 16

Sections 16:1-16:9

Chapter 17

Sections 17:1-17:5

The Electric Force & Coulomb’s Law

• The electric force is the force of attraction/repulsion between two or more charges

• The electric force can be calculated with Coulomb’s Law:

• k is called the “Coulomb’s Law constant”

• k = 9 x 109 N m2/C2

• Force is measured in Newtons

• Force is a vector so you must also include a direction!

E 2

kQQF =

d

Example 1: Coulomb’s Law

1. What is the magnitude of the force a +15 mC

charge exerts on a +3 mC charge 40 cm away?

E 2

9 -6 -3

E 2

kQQF =

d

(9x10 )(15x10 )(3x10 )F = 2531.25 N

0.40

Example 2: Forces in nature . . .

• Calculate the electrical force of attraction between a proton and an electron that are 1 cm apart.

• Compare this value to the gravitational force of attraction between the two particles.

E 2

9 -19 -19-24

E 2

kQQF =

d

(9x10 )(1.6x10 )(1.6x10 )F = 2.3x10 N

0.01

G 2

-11 -27 -3163

E 2

GmmF =

d

(6.67x10 )(1.67x10 )(9.1x10 )F = 1.01x10 N

0.40

The gravitational force is negligible when compared to the electric force!

Example 2: Net force in line

2. Find the resultant force on the +10 mC charge.

Example 3: Net force (Angles)

3. Find the resultant force on the +5 mC charge.

• Good website example: http://demo.webassign.net/ebooks/cj6demo/pc/c18/read/main/c18x18_11.htm

The Electric Field

Chapter 16

Sections 16:1-16:9

Chapter 17

Sections 17:1-17:5

The Electric Field

• Whereas a gravitational field (gravity) is the area around a mass, the electric field is the area around a charged particle.

• Arrows are used to represent the field around a mass or charge.

• The gravitational field always acts toward the center of the mass.

• The electric field acts in the direction that an imaginary positive charge of very small magnitude would travel.

• The “imaginary positive test charge” is a convention that is used to define many things in electricity.

• Here, we used the positive test charge to define the direction of the electric field lines.

Direction of Electric Field

• An imaginary positive test charge would be repelled from a positive charge. Therefore, the electric field lines point away from a positive charge.

• An imaginary positive test charge would be attracted to a negative charge. Therefore, the electric field lines point toward a negative charge.

Facts about Electric Field Lines

• Field lines are directed away from positive charge and toward negative charges.

• The density of the lines is proportional to the field strength.

• Electric field lines never cross.

Drawings You Should Know:

• You should be able to draw the electric field around two like and two unlike charges.

Field Lines from Multiple Charges

• Field lines can get crazy when multiple charges are involved!

• Use this animation to view field lines from multiple charges.

Calculating the Electric Field:

• The electric field, E, is a vector quantity; it has both magnitude and direction.

• Equation:

• Units: Newtons/Coulomb (N/C)

• The resultant electric field due to several point charges can be determined using the same method used in Coulomb’s Law problems.

2 2

kQ kQE = or

d r

Ex 1: Field created by 1 charge

1. Calculate the magnitude and direction of the electric field at a point which is 30 cm to the right of a -3 C point charge.

+q

9 -6

2 2

kQ (9x10 )(3x10 )E =

d 0.30

E = 300,000 N/C, left

Ex 2: Net Field - Particles in line

2. Two point charges lie along the x axis. A charge of +6.2 C is at the origin and a charge of -9.5 C is at x = 10 cm. What is

the electric field at x = -4 cm?

Explained in class or in written notes.

Ex 3: Net Field involving Angles

3. What is the electric field at point P shown below? (7.20 x 106 N/C, 56° N of E)

• Explained in class or in written notes

• Good website example: (scroll down, 2nd example)

http://demo.webassign.net/ebooks/cj6demo/pc/c18/read/main/c18x18_11.htm

Ex 4: Net Field - Simple Shape

4. Calculate the electric field at the upper, left-hand corner of a square 1 m on a side if the other three corners are occupied by 2.25 mC charges.

Ex 5: Net Field – More fun . . .

5. What is the magnitude of the net electric field at the center of the square, due to these 8 charged balls?

Electric Potential

Chapter 16

Sections 16:1-16:9

Chapter 17

Sections 17:1-17:5

Electric Potential

• Electric potential is defined as the potential energy per unit charge.

• It is very similar to gravitational potential energy in that is depends on location.

• Work was done to lift the boulder. The boulder now has potential energy.

• Work was done to move small positive charge toward the positive Van der Graff generator. The small charge now has potential energy.

Equipotential Lines • Locations that have the same potential energy are called

equipotential lines.

• Equipotential lines are similar to hills and valleys on a topographic map.

Equation for Electric Potential:

• Every equipotential line has an electric potential value.

• Variable for Electric Potential = V

• Equation:

• Units: Volts

• You must include positive and negative signs for charges in this equation!!!!!

• Electric potential is NOT a vector. This will make our calculations easy!

kQV =

d

Ex 1: Calculating Electric Potential

• Assume Q = -3 C.

• Calculate the electric potential at point B which is 0.40 meters from the surface of the charge.

• Calculate the electric potential at point A which is 0.60 meters from the surface of the charge.

Increasing or Decreasing?

• An imaginary positive test charge (green dot) would have zero potential energy (per unit charge) when next to a negative charge.

• The test charge’s potential energy (per unit charge) would increase if work was done to move the test charge further away from the negative charge.

Ex 2: Work done in Moving Charge

• Assume Q = -3 C.

• Calculate the work done to move an electron from point B to point A.

• Is this work positive or negative?

• (Sign convention: positive is defined as what happens naturally)

Ex 3: Intersection of Charges

• What is the electric potential at point A? (green dot)

• How is this similar to two mountains overlapping

• What is the electric potential at point B? (red dot)

• How is this similar to a hill and a valley overlapping?

Ex 4: Net Electric Potential

• What is the net electric potential at the origin?