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?