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2. 1 Charge & Coulomb's Law. Charge is a property of matter. There are two kinds of charge, .. 1 English rather than physics: An entity is something that exists. Physics General Physics II. Michael Fowler, UVa Physics, Fall Syllabus. Lecture Notes: Lecture 1: Introducing Electrostatics. Lecture 2: Coulomb's. Physics is the study of the fundamental laws of nature 2; Optics. The discussion of electromagnetic waves, as mani- fest by light, leads to an introduction to.

Due to symmetry the net magnitude of electric field along the x direction is zero. Appendix E Common Gaussian Surfaces 17 Electric Charge 2. Electric Fields 4. Electric Flux 5. Heller and K. Cooperative Group Problem Solving in Physics. University of Minnesota, Knight, Physics for Scientists and Engineers: Benjamin Cummings, Chabay, B. Electric and Magnetic Interactions, 3rd Ed. Young, R. Freedman, A. Ford, University Physics, 11th Ed. Addison-Wesley, Paul Hewitt, Conceptual Physics, 11th Ed.

Halliday, R. Resnick, J. Fundamentals of Physics Extended, 10th Ed. The context rich problems are designed such that the students are part of the story and are often required to interact with other people in preparing and reporting their solutions. Unlike in the typical end-of-chapter problems, students usually need to refine the definition of the problems, specify the unknowns, design their own problem-solving strategy, use several concepts, make assumptions, recall or invoke prior knowledge or "common-sense", supply additional information, perform experiments, and interact with experts and non-experts.

Discuss the rationale of solving context-rich problems in physics as articulated in the Introduction. Discuss the steps or framework for problem-solving and specify the template or distribute the problem-solving sheet.

Discuss the grading system for this particular activity. The recommended system is to grade each step, either in equal weights in the scale of 1 to 5 or 1 to 10 or in unequal weights, usually giving more premium to analysis than to the final answer. Allocating portions for peer- and self-evaluation in the final grade is also recommended. Group the students the recommended number is three to five students per group and arrange their seats the arrangement should be conducive for long discussions.

Due effort should be exerted to achieve heterogeneous distribution of students in terms of gender and class-performance. Encourage the students to device a system that would allow every member of the group to contribute to the discussion for every step and to rotate the roles among themselves, especially the role of secretary or scribe.

Arrange the schedule for problem solving and reporting to class. It is recommended that each group should solve at least one problem for each topic in this chapter.

Let the students spend the remaining class time to start solving the problems. Then they will have to solve the rest after the class and submit their final output later, e. If there is opportunity, group reporting of output in front of the class is recommended because it will allow students be familiar with problems that they are not assigned to solve. The steps they advocate, which is consistent or similar with those of the famous mathematician G. Polya, are as follows: They also have discussions and recommendation for the grading system, role assignment, and student distribution.

The major concept s being considered is indicated after the problem. You may design more problems considering the characteristics of context-rich problems described above. Your classmates often complain of painful electric shock whenever they open the door to leave the new fully-carpeted auditorium of your school. Write a letter to the principal about the problem explaining the physics behind the phenomenon and suggesting simple changes to the auditorium at least in the area near the door to prevent this nuisance.

You are a fieldtrip when a thunderstorm struck. Making matters worse, your school bus malfunctioned while it is in the middle of the road traversing a wide plain of rice fields. Convince your classmates that it is safer to stay inside the bus while waiting for help. Your friend told you about her problem.

She bought some replacement electronic parts for her personal computer a week ago and only found out yesterday that these were not working. When she tried to return them to the store, the salesman refused and told her it was her mishandling that ruined the electronic parts.

She said that she was careful that the devices were no subjected to vibrations. She said all she did was remove and throw away the metallic film-coated shipping bags that used to contain the devices. Explain to her why it is possible that indeed she is at fault. Your grandmother gave you silver-plated kitchen wares. These are old such that some parts of the plating are already worn off. Design an electroplating set up to restore this heirloom pieces. An energy saving advocacy group released an cartoon "infomercial" portraying old electric appliances as greedy monsters eating a lot of electric charges.

While you support their advocacy, you want their information to be accurate. Write a friendly letter to the advocacy group pointing out their error and suggesting some changes to their "infomercial. You are in charge of first aid during your Biology Club camping. Unfortunately, one of your club members got sick and dehydrated.

Explain to him why it is advisable to drink the sugar and salt solution that you prepared. You are an advocate of disaster prevention and preparedness. Use a van de Graaff generator to teach small children to be careful but not too afraid of thunder and lightning. Make sure that you explain the rules on safety in using the van de Graaff generator. You work in an architectural firm specializing in restoration of old building.

Convince your boss to invest in replacement of rusty and broken lightning rods in the building, explaining especially the effect of rust and breaks in the rod. You are a volunteer teacher in a first-aid class.

Demonstrate how to help a victim of electrocution and explain the reasons behind the various precautionary measures. You are discussing the hazards, risk and possible solutions of photocopiers and printers with the CEO and the building manager of your company.

The CEO asked you why there is bright light during photocopy, why print-outs are usually hot and if these heat sources can be avoided. You want that a separate air-conditioned room be set aside for photocopiers and printers. Create a cartoon or poster explaining the difference between an insulator and a conductor, particularly in terms of the mobility of the electrons, using as analogy e.

Electric potential energy 2. Electric potential 3. Equipotential surfaces 4. Electric field as a potential gradient 5. Electric potential Performance Standards The learners shall be able to use theoretical and experimental approaches to solve multi-concept and rich-context problems involving electricity and magnetism.

Learning Competencies At the end of the session, the students should be able to: Define operationally the electric potential; 2.

Draw and represent equipotential lines or equipotential curves. Calculate the electric potential due to a charge distribution. Prerequisite Knowledge electric field, electric force, electric charge, work done by a variable force Prerequisite Skills mathematical acumen in integration, variation analysis , drawing skill i.

Review the concept of work. Suppose an object is under the action of a constant force. Suppose an object travels from point A to point B. Suppose also that two constant opposite forces F1 and F2 act on the object. When might the net work done on the object be positive, negative, zero? Illustrate your answers. Now, suppose the charge in No. Determine the magnitude of the force F2 that must be applied to carry this out. You can do this in two ways: Rewrite your answer in No.

So that now, the electric potential V at a distance r away from a source charge Q is given by the expression: What makes this expression much easier to interpret than the expression for the electric field E? Find V 1. Draw where this V is measured in i 1 dimension, ii 2 dimensions, and iii in 3 dimensions. Inquire about the factors that affect the electric potential V. The locus of points having the same potential V is called an equipotential line or an equipotential curve.

Draw the equipotential lines around a positive source charge Q. Have the students calculate the total electric potential at the center of: A line segment of length 1. An equilateral triangle of side length 1. A square of side length 1. How did your answers in No. General Physics 2 Capacitors in Series and Parallel pt. Draw a circuit diagram of capacitors in series and in parallel; 2.

Explain what happens to the electric charge, voltage and capacitance for capacitors in series and in parallel; 3. Explain why a series connection is a voltage divider and why a parallel connection is a current charge divider; 4. Explain the use of capacitors in series and in parallel.

Inquire about the operational and geometric definitions of capacitance C. Have the students write down the meaning of each of the symbols present in the above definitions.

Present circuit diagrams of 2 capacitors in series and in parallel without actually mentioning the words series and parallel. Ask a student to differentiate the electric current across the circuits assuming the system of capacitors is connected to the same DC-voltage source.

Which circuit has the same current throughout? Which circuit has current that changes across the electric path loop? From the above circuit diagrams ask a student to differentiate the electric potential between the 2 circuits assuming the system of capacitors is connected to the same DC-voltage source. Which circuit has the same electric potential throughout? Which circuit has electric potential that changes across the loop s? At this point, allow the class to have discussion s according to groups.

Ask them to write their group answers on the blackboard whiteboard. Electric charge Q is a conserved physical quantity. This means that the total charge in a circuit stays the same. From 1, we see that charge Q splits or divides in a parallel connection.

What stays the same in a parallel connection? The answer is the electric potential V. Therefore, we have: What about the electric potential in a series connection? What does this equation mean? What happens to C as more and more capacitors are connected in series? What happens to C as more and more capacitors are connected in parallel? Draw the circuit diagram for this situation. From 1 and 2, why are c and d swapped in positions in terms of solving the unknowns?

Summarize your answers using a C-Q-V table like below: Define operationally capacitance; 2. Define geometrically capacitance; 3. Draw a schematic diagram of a capacitor; 4.

Identify certain types of capacitors. Prerequisite Knowledge electric charge, electric field, electric potential, dielectric Prerequisite Skills mathematical acumen in integration, variation analysis , drawing skill i. It would be best if there will be capacitors that the students can Actually see and touch Resources 1 Young and Freedman.

JPG 4 https: Show an image of a parallel-plate capacitor like the figure below Best to show an actual capacitor as a circuit element.

Fig 1. A parallel-plate capacitor 2. Have the students identify the parts of the parallel-plate capacitor shown above. Ask a student to compare and contrast the capacitors shown in the diagram below. Best to show different types of capacitors that the students can actually see and touch and identify.

Sample capacitors 2. Introduce the concept of capacitance. Capacitance is the ability of an object in this case a circuit element to store an electric charge Q. The circuit element that has this property is called a capacitor. The potential across the plates of this capacitor is then equal to the potential V of the power supply.

This is best illustrated in the diagram below. Charging a parallel-plate capacitor 2. Have the students explain: Ask a student what the unit of capacitance is. This unit is named after Michael Faraday. Ask a student to discuss the relationship among C, Q and V. Moreover, the capacitance C as a circuit element depends on the area A of each plate and the distance d between the plates. Ask a student to discuss the relationship among C, A and d. In a circuit, the schematic symbols for a capacitor is shown below: Some schematics for capacitors 9.

This is illustrated in the figure below: Electric field in a charged parallel-plate capacitor 33 What is the relationship between the electric field E and the electric potential V between the plates of the capacitor? Where is the energy stored in a parallel-plate capacitor?

Show that U is given by the expression: This is a simple exercise on integration. Have the students discuss in groups the result that happens when a dielectric is inserted between the plates of the parallel-plate capacitor. Have the students answer the following questions as guide to their analysis: Performance Standards The learners shall be able to: Use theoretical and, when feasible, experimental approaches to solve multiconcept, rich-context problems using concepts from electromagnetic waves, optics, relativity, and atomic and nuclear theory 2.

Solve problems involving interference and diffraction using concepts such as path length, phase difference , and path difference. Relate the geometry of the diffraction experiment set-up slit size, and screen to slit distance and properties of light wavelength to the properties of the diffraction pattern width, location of intensity of the fringes.

So far, we have concentrated on the aspects of light that can be explained by a particle model geometric or ray optics. We now need to examine the ways in which light behaves like a wave. We will examine the behaviour of water waves, and use the knowledge gained to make predictions of analogous behaviour of light as a wave, e. A ripple tank is usually a glass or transparent plastic container filled with shallow water.

You can start with 5 mm depth and then adjust the depth using glass plates. A substitute for this tank is a washbasin filled with shallow water. The following may be done as a demo, or as a challenge for students to perform.

A good detailed source is the Nuffield Foundation's website: Use a ripple tank to produce a spherical pulse by letting a water drop fall into a ripple tank.

Use a ripple tank to produce spherical waves by letting your finger go up down the water surface at regular intervals. Adjust the period of oscillation the time it takes your finger to repeat its up and down motion and see how the wavelength and speed changes as the frequency is changed.

You may use an image of the circular waves produced by letting your finger or a motorized cylinder to review the concept of wavelength, frequency, and wave speed.

Now let two droplets fall down simultaneously on two opposite sides of the ripple tank. Pay special attention to how the waves from each droplet combine at another point. This can be used as the starting point of the discussion of Huygens Principle. The demos from 5 onwards may be done on the same day, or on the other days when diffraction through a single slit and a double slit are discussed 4.

Use a ripple tank and a ruler with its edge bobbing up and down to produce plane waves on shallow water. Usually, a small motor is used to make the ruler or straight edge oscillate if we want plane waves. If the ruler is replaced by small cylinder bobbing up and down, one can produce circular waves.

If available, you can use a motor to automatically produce the water waves. The advantage of a motor is the frequency of oscillation can be regulated.

For manually driven water waves, we are usually limited to small frequencies. In succeeding lessons, you may use the ripple tank to produce refraction of waves. The way to produce this is to place a thin plate around 3mm so that there will be shallower and deeper portions on the ripple tank.

If you now generate a plane wave and make it travel towards the boundary between the deeper and the shallower edge, you can produce refraction in water waves.

You can adjust the angle of incidence and see how the angle of refraction changes as a result Ask students to observe the wavelengths. How does the wavelength change as the plane wave travels from deeper to shallower water? How does the frequency change as it goes from deeper to shallower water? How does the speed change as it goes from deeper to shallower water?

Longer wavelengths in deeper water. No change in frequency. Faster speeds in shallower water. To produce single-slit diffraction, one can place a divider with a slit for plane water to pass through. Adjust the slit size. As the slit gets larger, the diffraction effect gets smaller. To produce double slit diffraction, place a divider with two slits for plane water waves to pass through.

Ensure that the slit size is of the same order of magnitude as the wavelength of the water wave. In the following discussion, we will assume coherent sources. This means the sources should satisfy the following conditions: The goal is to extract Huygens Principle from the experiments.

Huygens Principle can be motivated using the droplet falling on the ripple tank. The landing point of the droplet acts as a source of a pulse or wave that propagates away from the source point.

If we have many sources, each of these sources must affect a point where the disturbance is measured. Huygens Principle may be stated in this way: Each point on a wavefront acts as a source of spherical waves.

For two point sources, we only need to add the contribution of two points. Suppose point A and B are two point sources with the same phase, frequency, and amplitude. Let point C be the observation point. On the other hand, if the phase difference is npi, then we have totally constructive interference. Instead of calculating everything using wavefunctions, it is helpful to just calculate the path length difference, if we want to find out if two point sources interfere constructively or destructively at the observation point..

Visualizing interference from two point sources.

Suppose you have two coherent point sources 3 cm apart. Call one point A, and call the second point B. Assume that the wavelength is 1 cm. Draw the two sources on a piece of paper, and ensure a 3 cm separation.

Use blue ink for the circles with center A, and black ink for circles with center at B. Points on which the circles intersect will be places where the waves will be at a maximum. Path difference change when passing through a medium with an index versus in air.

Final Exam

Optical path length when light is reflected by a medium with an index. If the medium that reflects has a higher index of refraction, then the phase is shifted by pi.

Assign a question similar to one of the sample questions. Check student work. This will require knowledge of hyperbolae. A hyperbola is defined as the locus of all points such that the difference of the distances from a point on the hyperbola to one focus APPENDIX A Sample Problem 1 Two sources of radio waves separated by a distance of 3k produce coherent waves of wavelength m.

As you walk in a straight line from one radio source to the other, the signal on your radio receiver alternately gets strong and weak. Calculate whether the signal is trong or weak after walking A. This means we have a strong signal B. This means we have a weak signal. This means we have a strong signal.

Sample Problem 2 X and Y in the Figure are coherent sources of 2 cm waves. The wavelength is 2 cm Will they interfere constructively or destructively at points A, B, and C? The sources vibrate in phase. Point P is 1 m from S1 and 3 m from S2.

S1 alone and S2 alone each produce a wave of amplitude A at P. Which one of the following is the amplitude of the resultant wave at point P when S1 and S2 are both emitting waves? Zero Answer: Sample Homework Visualizing interference from two point sources. Use blue ink for the circles with center at A. Use blue ink for the circles with center at B. Use black ink for the circles with center B. At points where the blue and black circles intersect, do the waves interfere constructively or constructively?

For exceptional students: What figure is formed from the locus of all points for which the path difference from A and B is equal to 0.

Sketch these figures using red ink. What figure is formed from the locus of all points for which he path difference from A and B is equal to an integer multiple of the wavelength? Sketch these figures for path difference 1cm, 2 cm, 3 cm. Sketch these figures using green ink.

If the sources are EM waves, and we place a line detector on the surface of the paper, locate the places where the detector finds constructive and destructive interference. Calculate the power consumption of a circuit element when the voltage applied and the current passing through the circuit element is known.

Concepts of Physics Part 2 - HC Verma Solutions

Calculate the power consumption of a resistor given two of the following: Relate the drift velocity of a collection of charged particles to the electrical current and current density. Draw a circuit diagram for a simple battery and bulb circuit.

Prerequisite Knowledge electric potential, potential difference , Leyden jars, electrostatic charging and discharge. Our goal is to explain electrical phenomena such as electric shocks. Ask students to give common situations where these technical terms -current, resistance, etc are used in everyday life. Draw possible ways of connecting the wire, the battery, and the bulb.

Ask students to identify which arrangements cause the bulb to light up. Draw the wire and battery setup. Ask students if the wire's temperature increased, decreased or stay the same.

State that today's lesson is about bringing together these observations, and to introduce operational definitions of current and resistance. Before the class starts, it would be useful to assign homework or do a lab activity. See Appendix 2 In a direct current simple circuit, the current is conventionally assumed to be a positive fluid flowing from the positive terminal of the battery, then through the bulb, and then through the wire, and then back to the negative terminal of the battery.

To make a complete circuit, we must also assume that charge flows from the negative terminal through the battery and then comes out again at the positive terminal. Current is the rate at which charge flows through a cross-sectional area of the wire or through a circuit element. In a simple circuit, current flow is the same all throughout, since we do not observe charge buildup at any point of the circuit. Wires heat up when current is passing through.

The heating effect, assuming fixed voltage, increases when the thickness of the wire decreases, or when the wire becomes shorter. This phenomenon is called Joule heating. Current depends on the applied voltage.

This is also called chordal resistance, since it is the slope of the line or chord connecting the origin of a current versus voltage graph to a point on the V-I curve. An early experiment on comparing resistances can be found in the Cavendish manuscripts.

Cavendish used a frictional generator to produce a fixed voltage relative to the ground, and thus a fixed amount of charge. He then let this charge pass through a metal wire, through his body, and then to the ground. The metal wires were varied in length and the kind of metal used.

Course Syllabus

By recording how painful the discharge was, Cavendish was able to rank objects by what we now know as resistance. A graph of V versus I can be used to characterize the current response of a circuit element to an 46 Teacher Tip: The goal is to extract, from experiments and a discussion of these experiments, the need for the concepts of current, resistance, resistivity, and conductivity. After these, we need to state the definitions.

See Appendix 1 for a possible discussion sequence. If the voltage is proportional to the current, the circuit element is said to be ohmic resistor. Voltage is proportional to current. The light bulb is not an ohmic circuit element, thus a calculation of resistance will show that it depends on the applied voltage.

An ohmic resistor, on the other hand, will show a linear V versus I graph that passes through the origin. An experimental way of determining whether a material is ohmic or not is to measure the current response of a circuit element to an applied voltage, and then plot the result. Plotting the current response of a light bulb versus the applied voltage is a good experiment for students to do, since it shows that making a linear fit to the graph is sometimes not appropriate.

Pouillet's law. The resistance of a wire is proportional to the length L of the wire inversely proportional to the cross-sectional area A. The proportionality constant is defined to be the resistivity rho. Conductivity sigma is defined to be the multiplicative inverse of resistivity rho. Resistance is temperature dependent. For small temperature intervals, the resistance has a linear dependence on temperature. Common electrical symbols need to be introduced.

See Appendix 3. For today, you will only need the following symbols: For the homework, you will need to include symbols for the voltmeter and ammeter.

Microscopic model of currents. Many currents can be interpreted as the motion of electrons. In resistors and wires, the current is due to electrons moving in the direction opposite to the electric field; that is, from lower to higher electric potential.

The electrons travel at an average velocity known as the drift velocity; the field does not increase the speeds, on average, since electrons also undergo collisions and lose energy.

The energy lost is macroscopically seen as Joule heating. The electron paths are modeled using a random walk, with drift. Assign a short exercise for students to solve in class. See Appendix 4. For each experiment, what concept needed to be defined. Write the symbols used for each concept, and the defining equations, with all symbols used identified. What is chordal and differential resistance? Electrical temperature sensors in phones and computers. Connect the light bulb, the battery, and the wire in as many ways as you can.

Sketch each of the possible ways in your notebook. For each arrangement, annotate if the bulb lights up or not. There should be at least four possible arrangements that make the light bulb light up. Draw these arrangements, and submit on the designated class meeting. Connect one end of the wire to the positive end of the battery this end usually has a plus sign and the other end to the negative end. Do this only for a short time, since it uses up the energy content of the battery.

This is known as shorting a battery. Equipped with numerical tools for constructing locally conserved operators that we introduce, we comprehensively explore the interplay of local interactions and disorder on localized edge modes in the XZX cluster Hamiltonian. This puts us in a position to challenge the narrative that disorder necessarily stabilizes topological order.

Syllabus for IGNOU BSc Physics - Mathematical Methods in Physics-II PHE-05

Contrary to heuristic reasoning, we find that disorder has no effect on the edge modes in the Anderson localized regime. Moreover, disorder helps localize only a subset of edge modes in the many-body interacting regime.

We identify one edge mode operator that behaves as if subjected to a non-interacting perturbation, i. This implies that in finite systems, edge mode operators effectively delocalize at distinct interaction strengths. In essence, our findings suggest that the ability to identify and control the best localized edge mode trumps any gains from introducing disorder. We consider lattices with N sites and quasi-periodic boundary conditions associated to an arbitrary twist K having simple spectrum but not necessarily diagonalizable.

In our approach the SoV basis is constructed in an universal manner starting from the direct use of the conserved charges of the models, i. Using the integrable structure of the models, incarnated in the hierarchy of transfer matrices fusion relations, we prove that our SoV basis indeed separates the spectrum of the corresponding transfer matrices.

Moreover, the combined use of the fusion rules, of the known analytic properties of the transfer matrices and of the SoV basis allows us to obtain the complete characterization of the transfer matrix spectrum and to prove its simplicity. Any transfer matrix eigenvalue is completely characterized as a solution of a so-called quantum spectral curve equation that we obtain as a difference functional equation of order n. Namely, any eigenvalue satisfies this equation and any solution of this equation having prescribed properties leads to an eigenvalue.

We construct the associated eigenvector, unique up to normalization, by computing its decomposition on the SoV basis that is of a factorized form written in terms of the powers of the corresponding eigenvalues. If the twist matrix K is diagonalizable with simple spectrum then the transfer matrix is also diagonalizable with simple spectrum. In that case, we give a construction of the Baxter Q-operator satisfying a T-Q equation of order n, the quantum spectral curve equation, involving the hierarchy of the fused transfer matrices.

In the groundbreaking Quantum Newton Cradle experiment [Kinoshita, Wenger and Weiss, Nature , , ], quasi-one-dimensional cold atom gases were observed with unprecedented accuracy, providing impetus for many developments on the effects of low dimensionality in out-of-equilibrium physics.Joseph Shing.

Ask the students to extend the definition in No. Fundamentals of Physics Extended 10th ed. Submit Search.

Physics 272 (General Physics II)

Yu Lead for Policy Advocacy and Communications: Ask each group to share one prediction. Mirrors paraxial approximation 3. We can define electric potential as follows when a unit charge is required to move from a point to another point against an electric field, the amount of work which is required is called electric potential.

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