Welcome to PHY2054C• Dr. Christos Velissaris Chris.Velissaris@ucf.edu

• Office hours: Tu.Th. 10:45am-11:45am (and before class) at PS160

• Book: “Physics” 9 ed. by Cutnell & Johnson, Volume 2.

• Two mid term exams (September 23 and October 28) and one comprehensive final (December 4). Iclicker questions in class.

• Grade: Midterm exam 15% each, Final 30%, iclicker participation 5%, Homework 15%, Lab 20%.

• Homework via the www.webassign.com web site. You must self enroll (see syllabus for name of class and access key).

• Class web site: www.physics.ucf.edu/~cvelissaris/Fall14/PHY2054 and at Webcourses.

2054 Class General Structure • The electric field, potential and DC circuits.

Medium difficulty.

• The magnetic field, induction and AC circuits.Very hard (the hardest of the class).

• The Electromagnetic Wave (light). Very easy.

• Geometrical optics and optical instruments.Hard but very interesting.

• Wave (physical) optics and wave phenomena.Very hard. New concepts and hard to visualize.

2054 Class Structure Part 1.• Electric charges, forces and Fields. (Ch 18)

The electric charge. Quantization and types of electric charge. Atomic structure. Conductors and Insulators. Coulomb’s law. The Electric Field and Electric field lines. Electric flux and Gauss law. Superposition of electric forces and fields.

• Electric potential and Capacitance. (Ch 19)Electric potential energy and electric potential. Equipotential surfaces. Capacitors. Energy stored in an Electric Field. Dielectrics.

• Electric Current, Resistors and circuits. (Ch 20)Electric current. Resistance and Ohm’s law. Resistors connected in series and in parallel. Capacitors in series and in parallel. Batteries, emf force and dc circuits. Energy and power consumed in dc circuits. The two rules of Kirchhoff for circuits. Ammeters and Voltmeters.

• The Magnetic Field. (Ch 21)Magnetic field and Magnetic field lines. Magnetic force on a moving charge and the right hand rule. Magnetic forces and torques on electric currents. Magnetic fields generated by electric currents. Solenoids and loops. Ampere’s law.

• Midterm Exam 1. (September 23)

2054 Class Structure Part 2.• Electromagnetic induction. (Ch 22)

Magnetic flux. Farady’s law. Lenz law. Transformation of electrical energy into kinetic and vice versa. Inductance. Self inductance and mutual inductance. Transformers. Magnetic field energy. AC motors and generators

• AC (alternating) currents (Ch 23)Phasors. Resistances, capacitative and inductive reactances. Impedance. Power consumed in an ac circuit. R-L, R-C and R-L-C circuits. Resonance.

• Electromagnetic waves. (Ch 24)Nature of light. Frequency, wavelength and speed of light. Radiation Energy and Pressure. Polarization of light.

• Midterm Exam 2. (October 28)

2054 Class Structure Part 3.• Reflection of light and Mirrors (Ch 25)

Flat and spherical (concave and convex) mirrors. Ray tracing and Mirror equation. Thin lenses. The mirror equation and the magnification equation.

• Refraction of light and Lenses. (Ch 26)

Index of refraction. Snell’s law and refraction of light. Dispersion of light. Lenses and ray tracing through lenses. The lens equation and the magnification equation. The human eye and defects of vision, the magnification lens and the microscope, the telescope.

• The Wave nature of light (Ch 27).

Young’s double slit experiment. Constructive and destructive interference. Diffraction of light and resolving power of optical instruments.

• Final Comprehensive Exam. (December 4)

2054 Class Structure Part 4

• Wave (physical) optics. (Ch 26)Superposition of waves. Constructive and destructive interference of light. Diffraction of light from a single and multiple slits. Resolving power (resolution) of an optical instrument.

• Final comprehensive exam. (December 5)

Chapter 18.• Electric charges and Fields.

• The electric charge. Quantization and types of electric charge. Atomic structure. Conductors and Insulators.

• Charge induction and polarization. Conductors and insulators in Electric fields. Capacitors.

• Coulomb’s law. The Electric Field and Electric field lines.

• Electric flux and Gauss law.

The electric charge• Electric charge is a fundamental property of matter.

Signifies that the particle carrying an electric charge participates in electromagnetic interactions.

• Known from antiquity electron = ηλεκτρον = amber

• Two types of electric charge, + and –. Electric forces can be attractive (opposite charges) or repulsive (same charges).

• Electric charge is conserved and quantized.

Electric charge and Matter.• Atom. Electrons orbiting a small nucleus

consisting of neutrons & protons.

• The electron carries negative charge equal and opposite to the charge of the proton. Neutrons carry no electric charge.

• The atom is electrically neutral. The number of electrons is equal to the number of protons (atomic number).

• Ion. A charged atom where an electron has been knocked off or acquired.

Ceq

kgm

e

e19

31

106.1

101.9

010675.1 27

n

n

qkgm

Ceq

kgm

p

p

19

27

106.1

10673.1

electron

proton

neutron

Which one of the following statements concerning the net electric charge on an object is true?

a) An object with a net negative charge has an excess number of protons.

b) The net charge can have any value greater than 1.60 1019

coulombs.

c) The net charge on an object is always a negative number.

d) Since protons are larger, a proton can carry more charge than an electron.

e) The net charge is quantized.

Poll Question

Conductors and Insulators

• Conductors. Materials where the outer electrons of the atoms are free to move from atom to atom (they don’t belong to a particular atom). Most metals. Charges move freely inside the conductor.

• Insulators. Electrons are associated with a particular atom. Very few electrons can move free in an insulator.

Charging the matter• We can charge matter by contact and/or

rubbing. Charged particles are transferred from one material to the other.

• Induction. External charges close to metals cause the free charges in the metal to be attracted or repelled.

• Polarization. External charges close to insulators disturb the symmetry of atoms which appear as dipoles (a positive and negative charge closely separated.

We can charge matter by contact and/or rubbing.

Charged particles are transferred from one material to the other.

Induction. External charges close to metals cause the free charges in the metal to be attracted or repelled.

Polarization. External charges close to insulators disturb the symmetry of atoms which appear as dipoles (a positive and negative charge closely separated.

The Coulomb force

229

221 10987.8 C

mNkr

QQkF

Coulomb in 1784 studied the electric force between two charged spheres and found:

Coulomb’s law is similar to Newton’s law of gravitation in several ways. Which one of the statements is not a similarity between these two laws?

a) In both laws, the force is inversely proportional to the square of the distance between two particles.

b) In both laws, the force decreases with increasing distance between the two particles.

c) In both laws, the force is proportional to the product of an intrinsic property of each of the two particles.

d) In both laws, the force is always one of attraction between the two particles.

e) In both laws, there is a proportionality constant that appears.

Poll Question

Experimental apparatus to test Coulomb’s law and measure the constant k.

Which of the following terms is used to describe a material that does not allow electrons to easily move through it?

a) conductor

b) resistor

c) transformer

d) insulator

e) inductor

Poll Question

If q = μ8.6 C =8.6 x10-6 C and d = 3.8 mm = 0.0038m determine the net force on charge 2.

A. 0 N

B. 46097 N to the right

C. 46097 N to the left

D. 20354 N to the left.

Exercise

Michael Faraday 1791-1867Every charge generates around it an Electric Field. The charged particle is never by itself. It is always accompanied by its own Field which generates the electric forces

The Electric Field.

The Electric Field.• This concept of “force” field was introduced to explain the

counterintuitive concept of action-at-a-distance (two bodies exercise each other a force while they are not in contact).

• Consider a charge Q. If we introduce an arbitrary “test” charge q at some distance r from the charge Q a Coulomb force |F| will be exercised on q (and vice versa). But |F|/q is constant (independent of the “test” charge q) as you can see from Coulomb’s law.

• We call the ratio |F|/q the Electric Field E generated by the charge Q.

• An (arbitrary) charge distribution generates an electric field around it. Any “test” charge introduced comes in “contact” with the Electric field and feels the Coulomb force.

The Electric Field - II.• The Electric Field is a “vector field” that is we

associate at each point of space a vector whose magnitude and direction depends on the charge distribution that generated the Electric Field.

• Electric Field lines: The set of lines with the property that the Electric Field at each point of the line is tangent to the line. They are lines of force.

• Orientation of the Electric field lines. They point from the positive charges towards the negative charges.

The electric field due to a single point like charge is:

An electron is a negatively charged particle that has a charge of magnitude, e = 1.60 1019 C. Which one of the following statements best describes the electric field at a distance r from the electron?

a) The electric field is directed toward the electron and has a magnitude of ke/r2.

b) The electric field is directed away from the electron and has a magnitude of ke/r2.

c) The electric field is directed toward the electron and has a magnitude of ke/r.

d) The electric field is directed away from the electron and has a magnitude of ke/r.

e) The electric field is directed toward the electron and has a magnitude of ke2/r.

Poll Question

Which of the following statements concerning the electric field is false?

a) The SI unit of the electric field is the newton per meter (N/m)

b) The electric field is a vector quantity.

c) At a given point, a charged particle will experience a force, if an electric field is present at that location.

d) If a positively-charged particle is placed at a location where the electric field is directed due north, it will be accelerated due north.

e) The magnitude of the electric field at a particular location due to a particular charged particle is inversely proportional to the distance of the particle from that location.

Poll Question

Which of the following combination of units are those for the strength of the electric field?

a)

b)

c)

d)

e)

2

2kg mC s

N mC

kg mC s

NC

C ms

Poll Question

• A charge Q is introduced in an Electric Field

What is the Coulomb force (magnitude and orientation) that the charge Q is going to feel?

E

EQF

Which of the following statements describes an object being charged by induction?

a) A glass rod is rubbed with silk.

b) A negatively-charged object is brought into contact with an initially uncharged conductor. When they are separated, both objects are negatively charged.

c) A rubber rod is rubbed with animal fur.

d) A positively-charged object is brought near with an initially uncharged insulator. The surface of the insulator becomes slightly negatively charged.

e) As you grab a door knob in the winter time, you feel a slight electric spark.

Poll Question

A conductor that is initially electrically neutral is touched by a rod that has a net positive charge. Which of the following statements describing the conductor after the rod is removed is true?

a) The conductor will have a net positive charge.

b) The conductor will electrically neutral.

c) The conductor will have a net negative charge.

Poll Question

Induction and Polarization • Induction. Redistribution of charges in a material

because of the presence of external charges (or external field).

• Polarization. The separation of the electron center of mass form the nucleus center of mass in an atom because of external charges. Atom behaves like an electric dipole.

• Electric Dipole. A positive and an equal negative charge separated by a distance D. Although the total charge is 0 an electric field is generated.

Conductors in external Electric Fields• If we place a conductor in an external Electric

Field, freely moving charges in the conductor will re-distribute themselves on the conductor’s surface until the TOTAL (external + induced) electric field inside the conductor becomes 0.

• Conductors are Electric Field “shields”.

• The freely moving charges in a conductor always accumulate themselves on the surface of the conductor.

Insulators in external Electric Fields

• If we place a insulator in an external Electric Field, the (atomic) dipoles in the material will orient themselves according to the direction of the external Electric Field. The TOTAL field in the insulator will be less than the external field but it will not become 0.

• Inductors do NOT “shield” from Electric Fields.

Capacitors

• Two parallel plates that carry equal and opposite sign charge.

• The electric field in the area between the plates is constant and uniform (electric field lines are straight lines).

• The electric field outside the area between the parallel plates is 0.

A uniform Electric Field exists everywhere in the x-y plane. The electric field has a magnitude of 4500 N/C and is directed at the positive x direction. A point charge -8x10-9 C is placed at the origin. Determine the magnitude of the net electric field at

a) y= 0.15 m and b) at x= -0.15m

A. 7700 N/C 5521.8 N/C

B. 1300 N/C 5521.8 N/C

C. 5521.8 N/C 7700 N/C

D. 1300 N/C 7700 N/C

Exercise.

Electric Flux.• Consider an Electric Field and an area A

(formed by a closed loop) inside the region with the field. Question: How much Electric Field is passing through the surface?

Electric Flux.

• Consider an Electric Field and an area A (formed by a closed loop) inside the region with the field. Question: How much Electric Field is passing through the surface?

• The answer depends on the strength of the field E, the size of the area and the orientation of the area relative to the orientation of the field.

Electric Flux.

cos AEE

n

n

Orientation of a surface in math is done with a unit vector n that is perpendicular to the surface:

Flux may be positive or negative. Flux sign shows the direction of the flow of theVector field through the surface, with respect to the chosen orientation of the Surface (where the unit vector n points)

cos AEE

n

n

n

n

n

If we have a CLOSED surface (like the one below) the orientation of the surface at some point of that surface is defined with the unit vector n that is normal to the surface at the point of interest and it points OUTSIDE the CLOSED surface.

Important

n

n

n n

Another example: Orientation of a spherical surface at various points of the surface. The unit vector n is not only perpendicular to the sphere but points OUTSIDE the CLOSED spherical surface.

Gauss Law

• The electric flux through a closed surface is equal to the TOTAL charge enclosed by the surface over the constant ε0.

0enclosed

closedQ

Remember the rule for the orientation of the closed surface. At some parts of theSurface the field flux may be positive and at other parts of the surface the flux may be negative.

The Electric Field inside a capacitor is:

0

E

Which one of the following statements concerning parallel plate capacitors is false?

a) The plates are made from metal.

b) One of the plates has a net positive charge and one has a net negative charge.

c) The electric field is proportional to the charge per unit area.

d) Electric field lines are directed from the negative plate to the positive plate.

e) The electric field lines between the plates are parallel and evenly spaced.

Poll Question

Application of Gauss law: Conductor with a hole and a charge in it.

Consider the field lines shown in the drawing. Which one of the following statements concerning this situation is true?

a) A is a positively charged particle and B is negatively charged.

b) B is a positively charged particle and A is negatively charged.

c) A and B are both positively charged.

d) A and B are both negatively charged.

Poll Question

A conducting sphere (shown in grey in the drawing) of radius R has a number q of excess electrons distributed uniformly over its surface. A spherically-shaped Gaussian surface with a radius r < R is represented in the drawing by the dashed circle. Applying Gauss’ law, what is the magnitude of the electric field inside the Gaussian sphere?

a)

b)

c) zero N/C

d)

e)

rq

04

204 r

q

rq

qr2

04

Poll Question

Surface 1 has an area of 1.7 m2 while surface 2 has an area of 3.2 m2. The Electric Field is uniform and has a magnitude of 250 N/C. Find the magnitude of Electric Flux through surface 1 and surface 2.

A. 348.1 Nm2/C 458.9 Nm2/C

B. 243.8 Nm2/C 655.3 Nm2/C

C. 243.8 Nm2/C 458.9 Nm2/C

D. 348.1 Nm2/C 655.3 Nm2/C

• There are two types of electric charges positive and negative. Same charges repel and opposite charges attract each other. Charge is conserved and quantized

• Coulomb’s law states that the force between two point like charges is given by:

• We can charge materials by rubbing, contact induction and polarization.

• An electric charge is always carrying an Electric Field which is depicted by the Electric Field lines. The Electric Field is a vector Field.

• Electric Field lines point from the positive charges towards the negative charges.

• If we have an Electric Field in space and we place a test charge in that field, the charge is going to feel an Electric Force given by F=QxE (Force = test charge X Electric Field.)

• A positive charge placed in an Electric Field will feel a force parallel to the field. A negative charge will feel a force opposite to the Electric Field.

• The Electric field of a point-like charge is:

• The Electric Flux through a surface is given by the formula Φ=A E cosθ. Θ is the angle between the electric field and the normal to the surface.

• Gauss’ Law. The electric flux through a closed surface is equal to Q/ε0 where q is the net charge inside the surface.

• Capacitor is a container of Electric Charge, Electric field and energy. Two parallel plates carrying equal and opposite charges constitute the simplest capacitor. The electric field inside such a capacitor is E=σ/ε0 wit σ the surface charge density on the plates σ =Q/A.

221

rQQ

kF

rQQ

kE 21

Chapter 18 Review