Electrostatics

Electrostatics Static Electricity Demonstrate how you can pick up the paper pieces without touching them in any way with your body. What is occurring at the atomic level that lets you do this? Static Electricity

Electrostatics Study of electric charges that can be collected and held in one place.

Ben Franklin

Electric Charge There are 2 kinds of electric charge, positive and negative. Interactions between + and – explain the attraction and repulsive forces Like charges repel and unlike charges attract. Electric charge is not created or destroyed; it is conserved. Charging is the separation, not creation, of electric charges.

Microscopic View of Charge The atom has positive charge in the nucleus, located in the protons. The positive charge cannot move from the atom unless there is a nuclear reaction The atom has negative charge in the electron cloud on the outside of the atom. Electrons can move from atom to atom without that much difficulty. Ernest Rutherford JJ Thompson

Methods of Charging Objects Charging by Friction Charging by Induction Charging by Conduction

Methods of Charging Objects 1. Charging by Friction • rub two different materials together • Since the two objects are made of different materials, their atoms will hold onto their electrons with different strengths. • As they pass over each other the electrons with weaker bonds are “ripped” off of that material and collect on the other material.

How can a charged object and a neutral object attract?

Conductors and Insulators Charges transferred to one part of an insulator remain on that part. Insulators include glass, dry wood, plastics, and dry air Charges added to a conductor quickly spread over the surface of the object. In general, examples of conductors include graphite, metals, and matter in the plasma state

Conductors and Insulators The charges are NOT free to move around Conductor Many of the charges free to move around

Insulators and Conductors glass rubber oil asphalt fiberglass porcelain ceramic quartz (dry) cotton (dry) paper (dry) wood plastic air diamond pure water Semiconductors: Silicon Germanium carbon Conductors: silver copper gold aluminum iron steel brass bronze mercury graphite dirty water concrete

How can a charged object and a neutral object attract?

How can a charged object and a neutral object attract?

How can an Insulator be Polarized?

Insulators and Conductors

A is either + or neutral; C is - 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 conclusively confirm about the charge on balloon A and C for each situation. A is either + or neutral; C is - A is + and C is +

Upon entering the room, you observe two balloons suspended from the ceiling. You notice that instead of hanging straight down vertically, the balloons seems to be repelling each other. You can conclusively say ... a. both balloons have a negative charge. b. both balloons have a positive charge. c. one balloon is charge positively and the other negatively. d. both balloons are charged with the same type of charge. Explain your answer.

Two objects are shown below. One is neutral and the other is negative Two objects are shown below. One is neutral and the other is negative. Object X will ____ object Y. a. attract b. repel c. not affect A + -

Charge Charge is quantized comes in two forms which Ben Franklin designated positive (+) and negative (-) Charge is quantized Smallest possible charge, designated e, is the magnitude of charge on 1 electron (-e) or 1 proton (e). e is referred to as the elementary charge e = 1.602 x 10-19 C The coulomb is the SI unit of charge

Sample Problem A certain static discharge delivers -0.5 C of electrical charge. How many electrons are in this discharge?

Electric Force non contact force large compared to gravity attractive or repulsive depending on charges depends on distance can be analyzed using free body diagrams and Newton’s laws

Electric Force An insulating rods with small conducting spheres suspended by thin wires. Coulomb charged the spheres by conduction and measured and quantified the electric force. 1785 French physicist, Charles Coulomb

Distance between charges Coulombs Law Charge MAGNITUDE Distance between charges SI units of Force: Newton (N) SI units of Charge: Coulomb (C) SI units of distance: meters (m) 1 C is the charge on 6.24 x 1018 electrons charge of 1 e-, e = 1.6 x 10-19 C (elementary charge) k = 9.0 x 109 Nm2/C2

Coulomb’s Law Electrical Forces in Atoms Because most objects have almost exactly equal numbers of electrons and protons, electrical forces usually balance out. Between Earth and the moon, for example, there is no measurable electrical force. Although electrical forces balance out for astronomical and everyday objects, at the atomic level this is not always true. Often two or more atoms, when close together, share electrons. Bonding results when the attractive force between the electrons of one atom and the positive nucleus of another atom is greater than the repulsive force between the electrons of both atoms. Bonding leads to the formation of molecules.

The diagrams show two charged objects and their separation The diagrams show two charged objects and their separation. Rank the force that the left object exerts on the right object from the STRONGEST to WEAKEST force. Explain how you made the ranking. A > B > C A) B) C) + 2q d + 3q + q d + q d

The diagrams show two charged objects and their separation The diagrams show two charged objects and their separation. Rank the force that the left object exerts on the right object from the STRONGEST to WEAKEST force. Explain how you made the ranking. A = B = C A) B) C) - q d + q d + q - q d

The diagrams show two charged objects and their separation The diagrams show two charged objects and their separation. Rank the force that the left object exerts on the right object from the STRONGEST to WEAKEST force. Explain how you made the ranking. C > A > B A) B) C) + q d + q 2d + q ½ d

The diagrams show two charged objects and their separation The diagrams show two charged objects and their separation. Rank the force that the left object exerts on the right object from the STRONGEST to WEAKEST force. Explain how you made the ranking. C > A > B A) B) C) + q d + 2q + q 2d + 3q 1/3 d What is

Compare the force that the left charge exerts on the right to the force that the right exerts on the left. Explain. + q d + 2q - q 2d What is + 2q + q 1/3 d C > A > B

Do Now: Two charged spheres 10cm apart (0 Do Now: Two charged spheres 10cm apart (0.1m) attract each other with a force of 3.0x10-6 N. What force results from each of the following changes , considered separately? Both charges are doubled and the distance remains the same. The separation is increased to 30 cm Coulombs Law

Coulombs Law only valid for point charges (or uniformly charged spheres) applies to objects whose size is much smaller than the distance between them describes the force between 2 charges when they are at rest. The study of charges at rest is called electrostatics. Coulombs law gives force on a charge due to only one other charge. If more than one charge present, Fnet is the vector sum or SUPERPOSITION of each Coulomb force.

Sample Problem: Sphere A with charge +6 mC is located 0 Sample Problem: Sphere A with charge +6 mC is located 0.04 m from another sphere B with charge -3mC. What is the force of sphere B on A? 0.04m A B FAB 6mC -3mC towards B

Sample Problem: Electric force on electron by proton: Determine the magnitude of the electric force on the electron of a hydrogen atom exerted by the single proton that is its nucleus. Assume the electron orbits the proton at its average distance of r = 0.53 x 10-10 m. + Fep qe = 1.602 x 10-19 C

Sample problem Two identical positive charges separated by 12.5 cm (0.125 m) exert a repulsive force of 1.24 N on each other. What is the magnitude of each charge? 0.125m q q F F = 1.24N

+3.5 x 10-8 C and -2.9 x 10-8 C when separated a distance of 0.60 m. Problem: Determine the electrical force of attraction between two balloons with separate charges of +3.5 x 10-8 C and -2.9 x 10-8 C when separated a distance of 0.60 m. +Q1 -Q2 d=0.60m towards the other balloon

Superposition Electrical force, like all forces, is a vector quantity. If a charge is subjected to forces from more than one other charge, all the forces must be added using vector addition. Vector addition to find the resultant vector is sometimes called superposition.

Scalars and Vectors All measurements are considered to be quantities. In physics, there are 2 types of quantities – SCALARS AND VECTORS. Scalar quantities have only magnitude. Vectors are quantities that have magnitude and direction. time mass temperature displacement Magnetic Field acceleration Force velocity Gravitational Field

Vectors are used to describe motion and solve problems concerning motion. For this reason, it is critical that you have an understanding of how to represent vectors add vectors subtract vectors manipulate vector quantities.

Vectors tip 8 units 2 units 5 units tail Magnitude represented by the length of the vector

Vectors y 1200 800 00 2250 300 600 from -x 3000 x -600 450 from-y Direction represented by the direction of the arrow

Adding Vectors - + Dx = +4 mi + (-7 mi) = -3 mi We know how to add vectors in 1-dimension. Example: If someone walks 4 mi east and then 7 mi west, their total displacement is 3 mi west. Adding vectors mathematically – In one dimension, assign direction + or – and add algebraically west - east + Dx = +4 mi + (-7 mi) = -3 mi Direction matters (if was 7 mi west ….) 1-D, direction is indicated with + and - and then the vectors are added algebraically Adding vectors graphically – TAIL TO TIP 3 mi 4 mi 7 mi

Adding Vectors What about if the vectors are in different directions? For example, what if I walk 5 steps north and then 4 steps east. What is my total displacement for the trip? OR what is the vector sum of the 1st displacement (5 steps north) and the 2nd (3 steps east)? 4 steps east Dx = ? 5 steps north

Adding Vectors “tail to tip” Dx q To add the vectors graphically North 4 steps east To add the vectors graphically Draw the first vector (5 steps north) beginning at the origin. Draw the second vector (3 steps east) with its tail at the tip of the first vector. Draw the Resultant vector (the answer) from the tail of the first vector to the tip of the last. 5 steps north Dx q West East South

http://phet.colorado.edu/en/simulation/vector-addition

Determine the net electrical force on sphere A Sample Problem- Determine the net electrical force on sphere A Fnet 0.2m 0.6m A B C FAB FAC 2mC -3.6mC 4mC Fnet= (all the forces to the right) –(all the forces to the left)

How to solve problems using Coulombs Law Make a diagram of the problem Make a force diagram of all the forces acting on the particle in question. Identify the direction of the force using the rule that opposite charges attract and like charges repel. Use Coulomb’s Law to calculate the magnitude of each of the forces acting on the particle of interest. This means ignore the + and – signs on the charges when doing the math. Find the total or net electric force on the particle of interest by adding the forces as vectors.

Sample Problem- A charge of 6 Sample Problem- A charge of 6.00 mC is placed at each corner of a square 1.00 m on a side. Draw the forces acting on charge and determine the direction of the net force on charge 2. Fnet F23 F24 1 1m F21 2 VERY important to keep in mind that Coulombs law gives force on a charge due to only one other charge. If several or many charges are present, the net force on any one of them will be the vector sum of the forces due to each of the others. For students – find net force on sphere B 4 3

Sample Problem- Three point charges of magnitude +1 C, +1 C and −1 C respectively are placed on the three corners of an equilateral triangle as shown. - Which vector best represents the direction of the net force acting on the −1 C charge as a result of the forces exerted by the other two charges? Fnet + + a) b) c) d)

Sample Problem- A +6 mC and a -3 mC charge are placed 25 cm (0 Sample Problem- A +6 mC and a -3 mC charge are placed 25 cm (0.25m) apart. Where can a third charge be placed so that it experiences no net force – to the left, in the middle or to the right of the charges? 0.25m A B 6mC -3mC

Concepts Two charged objects have a repulsive force of 0.080 N. If the charge of one of the objects is doubled, then what is the new force? 0.16 N Two charged objects have a repulsive force of 0.080 N. If the charge of both of the objects is doubled, then what is the new force? 0.32 N Two charged objects have a repulsive force of 0.080 N. If the distance separating the objects is doubled, then what is the new force? 0.02 N

The Electric Field

Electric Field The presence of a charge modifies empty space. This enables the electrical force to act on charged particles without actually touching them. We say that an “electric field is created around the charged particle. If a charged particle is placed in an electric field created by other charges, it will experience a force as a result of the field. We can calculate the electric force from the electric field. http://phet.colorado.edu/en/simulation/charges-and-fields

Electric Field The electric field produced by a positive charge is directed away from the charge A positive test charge would be repelled from the positive source charge

Electric Field The electric field produced by a negative charge is directed toward the charge A positive test charge would be attracted to the negative source charge - + -

Electric Field Lines The arrows in a field are not vectors, they are “lines of force”. The electric field lines indicate the direction of the force on a positive test charge placed in the field. Negative charges experience a force in the opposite direction. -

Electric Field Lines The closer the field lines, the stronger the field. The number of field lines leaving or terminating on a charged object is proportional to the magnitude of its electric charge.

Electric Field around Charge Electric field lines are directed away from positive charges and toward negative charges. + + - -

Why use fields? Forces exist only when 2 or more particles are present. Fields exist even if no force is present. The field of one particle only can be calculated.

Electric Field Q is the source charge that produces E The force on a charged particle placed in an electric field is easily calculated q is a test charge in the electric field produced by Q Fel Q is the source charge that produces E Q E depends only on the source charge, Q E is a vector SI Units are N/C

Approximate Values of Typical Electric Fields Value (N/C) Near a charged, hard-rubber rod 1 x 103 In a TV picture tube 1 x 105 Needed to create a spark in air 1 x 106 At an electrons orbit in a hydrogen atom 1 x 1011

http://media. pearsoncmg http://media.pearsoncmg.com/bc/aw_young_physics_11/pt2a/Media/Electricity/1104PointCharge/ElField.html http://media.pearsoncmg.com/bc/aw_young_physics_11/pt2a/Media/Electricity/1104PointCharge/Main.html

Sample Problem A positive test charge of 5.0 x 10-6 C is in an electric field that exerts a force of 2.0 x 10-4 N on it. What is the magnitude of the electric field at the location of the test charge? + F = 2x10-4 N q = 5.0mC in the same direction as the force (since test charge is positive)

Sample Problem What is the electric field strength at a point that is 0.30 m to the right of a small sphere with a charge of -4.0 x 10-6 C? Q = -4.0 mC E = ? d = 0.30 m The field’s direction is to the left, into the negative charge

Sample Problem A negative charge of 2.0 x 10-8 C experiences a force of 0.060 N to the right in an electric field. What are the fields magnitude and direction in that location? - + F = 0.060 N - q = -2.0 x 10-8 C The field’s direction is to the left, (opposite to direction of force on negative charge since neg charges move opposite the direction of the E field lines)

+ + - Which electric field is the strongest? b a) b) c) What is the sign of the charges that produce the electric fields shown?

Picturing the Electric Field Electric field between 2 opposite point charges Electric field around a point charge Electric field between charged plates http://phet.colorado.edu/en/simulation/charges-and-fields

Electric Field Line Patterns An electric dipole consists of two equal and opposite charges The high density of lines between the charges indicates the strong electric field in this region

Electric Field Line Patterns Two equal but like point charges At a great distance from the charges, the field would be approximately that of a single charge of 2q The bulging out of the field lines between the charges indicates the repulsion between the charges The low field lines between the charges indicates a weak field in this region

Electric Field Patterns Unequal and unlike charges Note that two lines leave the +2q charge for each line that terminates on -q

Superposition When more than one charge contributes to the electric field, the resultant electric field is the vector sum of the electric fields produced by the various charges. Again, as with force vectors, this is referred to as superposition.

Problem A particle with charge -5.0 μC is placed at -2.0 m, and a particle with charge 5.0 μC is placed at +2.0m. What is the electric field at the origin? q1=-5mC q2=+5mC E1 2m 2m q1 q2 E2 direction

Picturing the Electric Field The magnitude of the electric field at any point is not the field line itself, but can be determined from the field line. The direction of the electric field is always tangent to the field line at any given point. Electric field and force are vectors and vectors are never curvy. The strength of the electric field is related to the spacing between the field lines. The field is strong where the lines are close together. The electric field lines do not represent the path a test charge would follow, they represent the direction of the electric force on a particle placed in the field. How measure electric field? Test charge – place test charge at some location and if there is an electric force on it, then there is an electric field there. Tesst charge must be small enough so that doesn’t affect the other charges Draw on board 2 opposite charges and fields Field lines always LEAVE A POSITIVE CHARGE AND ENTER A NEGATIVE CHARGE The never cross