Phy252 by Chem Engine

PHY 252-ELECTRICITY AND MAGNETISM II (2 CREDITS-CORE) Course duration: 2 hours lecture per week for 15 weeks (30h) As taught in 2011/2012 session

2.0

LECTURER DETAILS: DR. A.B. Alabi B.Sc.(Physics)Ile-Ife, M.Sc., Ph.D.( Physics) Ilorin remialabi70@unilorin.edu.ng; rems050970@yahoo.com ROOM 5G21, Department of Physics, Faculty of Science, University of Ilorin, Ilorin, Nigeria

Consultation Hours: Tuesdays and Thursdays 12 noon – 3:00pm

3.0 COURSE DETAILS 3.1 Course Content: Linear circuits and DC bridges, AC networks, magnetic induction, transients, Biot-Savart’s law, Lorentz force, Faraday’s law, AC motors and generators, the triode, junction diode, transistor amplifier, diode rectification, power supply. 3.2 Course Description: Linear circuits and DC bridges: Charge transport and current density, Electrical conductivity and Ohm’s law, resistance of conductors, circuits and circuit elements, electromotive force and the Voltaic cell, variable currents in capacitors, resistors and inductors. AC networks: Alternating current, resonant circuit, admittance and impedance. Magnetic induction: Magnetic field, field of current-carrying wire, fields of rings and coils, BioSavart’s law, Lorentz force, Faraday’s law, AC motors and generators. Semiconductors: Types, conductivity and applications in triode, junction diode, transistor amplifier, diode rectification, power supply. 3.3 Course Justification: This course is designed for students to understand the features and behavior of electric charges in materials and fields. It will help students to understand various applications in which the force generated can be applied. 3.4 Course Objectives: At the end of the course, students should be able to : Define and describe charge transport in materials, understand the network of electric transfer and the components both active and passive. Calculate various parameters concerning charges. State

and describe the laws on interaction of current and fields. Understand the applications of the effects of current transfer in fields and materials.

At the end of the course, the students will be able to:       

Identify different components of an electric circuit and functions. Determine the value of quantities of current, charges, voltage in a circuit. Understand the networks of circuit and calculate quantities such as impedance. Understand the concept of magnetic field and derivation of their magnitude. Know the principles/laws about the motor and induced emf. Understand conductivity in materials with respect to temperature and nature. Know the applications of materials in electronic devices.

3.5 Course Requirements: PHY 252 is Compulsory for all 200L students of Physics. A student must have nothing less than 75% attendance at lectures to be qualified to take the final examinations. 3.6 Methods of Grading: Continous assessment -30 % Examinations -70% Total 100% 3.7 Course delivery strategies and practical schedules: Course delivery will be by face to face Lecture method. Continuous assessment will be given in the first hour of week 7 and 14. Assignment will be given to students which must be submitted.

4.0 LECTURE CONTENT Weeks 1 - 3:

Linear Circuits, Dc Bridges And Transients

Objective: At the end of the week, students should be able to explain the concept of current density, have a microscopic picture of charge transport by ions. To make student know the electric components and circuits, variation of current in circuits with different components and be able to solve problems. Description: The students will be taught basics and treat questions on electric current, current density, Ohm’s law, Resistivity, electromotive force, electric circuits, Kirchhoff’s law, RC, LR and RLC circuits, power dissipation in circuits. Hour 1 

Electric current



current density

 

Ohm’s law Resistivity

 

Electromotive force Electric circuit

 

Kirchhoff’s law Transient

Hour 2

Hour 3

Hour 4

Hour 5 

RC, RL and RLC circuits.



Power dissipation in circuits

Hour 6

Study Questions: 1. Definition of current density and estimation (i) Show that Ohm’s law can be written as J = E/ρ J = Current density, E = Electric field and ρ = resistivity. 2. A current of 10 A flows through a wire of 1 mm2 cross-section. If the density of charge carriers in the wire is 1027 m-3, Find the average drift velocity of the electrons. Given that electronic charge is 1.6 x 10-19 Coulomb. 3. (a) State Kirchhoff’s laws (b) Find the current in each segment of the circuit I1, I2 and I3. R2 I1

B + R1

E1 -

R3 I2

Given that E1 = 10 V, E2 = 6 V, R1 = 2 Ω, R2 = 4 Ω, R3 = 1 Ω, and R4 = 3Ω.

4. Consider a discharging RC circuit in which the initial charge on the capacitor is qo = EC . Show that the charge on the capacitor at time t after the switch was closed is q(t) = qo e-t/RC and that the current in the circuit at time t is I(t) = E/R e-t/RC . 5. An electronic unit consist of a 40 kΩ resistor in series with a 120 µF capacitor and a 10 V battery. If at t = 0 the switch is closed. (i) How much time elapses before the current through the resistor drop to 1/e2 of its initial value (ii) what charge is on the capacitor when t is 0.5 resistive time constant.

Reading list: 1. Electricity and magnetism by S.G. Starling and A.J. Woodall (1962), William Clowes and Sons Ltd, London, Revised Edition, pp. 47 – 104, 305 – 384. 2. Fundamentals of Electricity and Magnetism by Arthur F.K. (1969) McGraw – Hill Inc. pp. 162 – 316, 382 – 431, 506 – 517.

Week 4:

AC – Networks

Objectives: By the end of the week, students should be able to AC network and solve problems dealing with impedance and admittance of the circuit. They must understand the concept of resonance. Description: Alternating The students will be taught alternating current with resistor, capacitor and Inductor and RLC circuits, power in AC circuits, resonance and filters. Study questions: 1. A single-loop RCL circuit contains an AC generator. VR, VC and VL are the time-varying potential differences across the resistor, the capacitor and the inductor respectively. Let L= 60 mH, frequency = 60Hz and Em = 300 V. Find VL,M 2. Find XL in question 1 above. 3. Find iL,M in question 1 above. 4. A steady emf (E0 = 120 V) is applied to a single-loop resistive circuit with R =150 Ω. What is the power dissipation. 5. Write a short note on resonance in AC circuit. Reading list: 1. Electricity and magnetism by S.G. Starling and A.J. Woodall (1962), William Clowes and Sons Ltd, London, Revised Edition, pp. 47 – 104, 305 – 384.

2. Fundamentals of Electricity and Magnetism by Arthur F.K. (1969) McGraw – Hill Inc. pp. 162 – 316, 382 – 431, 506 – 517. 3. David Halliday and Robert Resnick (1978), John Wiley and Sons Ltd., pp. 675 – 805, 857 – 872.

Weeks 5 and 6 : Magnetic Induction, Lorentz Force And Faraday’s Law Objectives:

Student are expected to understand the concept of magnetic induction, the force generated by magnetic field and the principle guiding the induction of current in conductors.

Description: Student will be taught the concept of magnetic field produced by moving electric charges and electric current. Lorentz force exerted on moving electric charges will be defined and explained. Effects of moving wire in magnetic fields will be described, induced emf, Faraday and Lenz laws shall be discussed. Hour 1

Moving charges and magnetic field

Hour 2

Magnetic force and Ampere’s law

Faraday’s law

Hour 4

Lenz’s law

Study Questions: 1. State Faraday’s law 2. State Lenz’s law 3. Two long parallel wires A and B are 15cm apart and carry currents of 5A and 3A respectively. Find the force on a 2m length of wire B, if the currents are parallel. 4. A solenoid is 1.0 m long and 3.0 cm in inner diameter. It has five layers of windings of 850 turns each and carries a current of 5.0 A. What is the magnetic field B at the center. 5. What is the magnetic flux ϕB for a cross section of the solenoid (in question 4 above) at its center.

Week 7: Biot – Savart’s Law Objectives: It is expected that student will understand relation between current and magnetic field and to be able to derive the value of the magnetic field from a distance. Description: The students will be taught about the magnetic field generated by a steady current I (a constant flow of electric charges in which charge is neither accumulating nor depleting at any point) described by the Biot–Savart law:

They will also be taught how to obtain the magnetic field at a distance from conductors. Hour 1: Hour 2:

Explanation of the concept of Biot – Savart’s law Derivation of the magnetic field at a distance r from a straight conductor and a conducting loop.

Study Questions: 1. State Biot-Savart law. 2. Derive the magnitude of the magnetic field from a straight 3. Derive the magnitude of the magnetic field from the circular loop. 4. State the expression for the magnetic field dB at a distance from a conductor that resulted from a current element idV according to BiotSavart law. dB





idl



4

sin r 2



Show that the magnetic field “B” at a distance x along the axis of conducting loop of radius R, carrying a current I is

Bx 

o I 2

R2 (x2



R2 )

Week 8: AC and DC Motors Objectives: This will assist the students to understand the basic principles responsible for the conversion of electrical energy to mechanical energy and mechanical to electrical energy. Description: This lecture is meant for student to understand motor principle and the laws guiding its operations. Hour1 We consider motors – which convert electrical energy into mechanical energy, operating through the interaction between a magnetic field and a set of windings simple DC motor has a coil of wire that can rotate in a magnetic field. The current in the coil is supplied via two brushes that make moving contact with a split ring. The coil lies in a steady magnetic field. The forces exerted on the current-carrying wires create a torque on the coil. Hour2 Alternating Current generation and components. Study Questions: 1. Describe an AC motor. 2. Describe a DC motor. 3. Distinguish between an AC and a DC motor. 4. Consider a coil 2.0 cm high and 1.0 cm wide, it has 250 turns and is mounted so that it can rotate about a vertical axis in a uniform radial magnetic field with B = 2000 gauss. A spring provides a counter-torque that cancels out the magnetic torque, resulting in a steady angular deflection ϕ corresponding to a given current i in the coil. If a current of 1.0 x 10 -4 A produces an angular deflection of 30°, what is the torsional constant κ of the spring. 5. A galvanometer of resistance 15 Ohms gives a full scale deflection to a 5 mA current. How would the galvanometer be modified to measure (i) 5.0 A (ii) 50 V.

Week 9:

Generators

Objectives: This will assist the students to understand the basic principles responsible for the conversion of electrical energy to mechanical energy and mechanical to electrical energy.

Description: – –

In this lecture we consider rotating electrical machines generators which convert mechanical energy into electrical energy. The alternating signal from the earlier AC generator could be converted to DC using a rectifier A more efficient approach is to replace the two slip rings with a single split slip ring called a commutator

Study questions:

Describe the principle used in generating induced emf in a conductor. Distinguish between a DC generator and an AC generator. 3. What is meant by the root mean square value of a current or voltage. 4. The armature of an AC generator rotates at a frequency of 60Hz and develops an emf of 120 V (root mean square value). The coil has an area of 2.0 x 10 -3 m2 and consist of 400 turn. Find the magnitude of the magnetic field in which the coil rotates. (note: Erms = E0/√2 ). 5. A wire 1.0 m long carries a current of 10 A and makes an angle of 30° with a uniform magnetic field with B = 1.5 T. Calculate the magnitude and direction of the force on the wire. 2.

Week 10:

Semiconductor Materials

Objectives: This is for the student to know classes of materials with emphasis on semiconductor materials, its properties and how their features can be modified. Description: The students shall be taught that Semiconductor is the class of material where the conductivity of the material can be controlled to vary a large orders of magnitude. –Elemental semiconductor: Si, Ge –Compound semiconductor (fixed composition): SiC, GaN, GaAs, InP –Alloy: Si1-xGex, Al1-xGaxAs, Hg1-xCdxTe

Study questions: 1. Describe a semiconductor material using the energy band theory and give five examples. 2. What is meant by intrinsic extrinsic conductivity. 3. Define doping. 4. Write short note on electron-hole pair. 5. What is meant by depletion layer.

Week 11:

Junction Diode

Objective: Students are expected to understand the formation of diode using different types of semiconductor materials. They understand the movement of charge carriers across the junction and the effect of barrier. Application of the diodes are also important for student. Description: The student will be taught the following: The simplest semiconductor device is a pn junction diode, The interface between an n-type region (doped ND) and a p-type region (doped NA), Built in voltage (Vbi) results from the balancing of the drift current due to minority carriers, and the diffusion current due to majority carriers. We do not directly measure the voltage Vbi, but rather the potential difference between the two Fermi levels. We can change this equilibrium, and thus generate current, by applying a voltage to the diode, or shinning light on the diode. Applying a positive voltage decreases the potential barrier of the p-n junction correspondingly. I = Io ( exp(V / UT) - 1 ) o Forward bias is when V > 0, resulting in more diffusion current: I = Io exp(V / UT) o Reverse bias is when V < 0, resulting in more drift current: I ~ - Io For this reason, Io is often referred to leakage current of a p-n junction. Study Questions: 1. Describe how a p-n junction diode is produced. 2. Describe the usage of diode or combination of diodes to produce half-wave and full-wave rectification. 3. Given that a p-n junction diode draws 50 mA current when a 0.25 V forward bias is applied at a junction temperature of 200째C. Compute the saturation current of the diode and its dynamic resistance. 4. Draw the I-V characteristic curve for a junction diode 5. Describe a Zener diode.

Week 12:

Transistor Amplifier

Objectives: At the end of the lecture students should understand the concept of amplification using the transistors. They should be able describe in detail the transistor.

Description: The student will taught that common-emitter amplifier is designed so that a small change in voltage in (Vin) changes the small current through the base of the transistor; the transistor's current amplification combined with the properties of the circuit mean that small swings in Vin produce large changes in Vout. Various configurations of single transistor amplifier are possible, with some providing current gain, some voltage gain, and some both.  Study Questions. 1. Describe the transistors 2. Describe the Field effect Transistor 3. Explain the application of a transistor in amplification. Reading list: 1. Electricity and magnetism by S.G. Starling and A.J. Woodall (1962), William Clowes and Sons Ltd, London, Revised Edition, pp. 47 – 104, 305 – 384. 2. Fundamentals of Electricity and Magnetism by Arthur F.K. (1969) McGraw – Hill Inc. pp. 162 – 316, 382 – 431, 506 – 517. 3. David Halliday and Robert Resnick (1978), John Wiley and Sons Ltd., pp. 675 – 805, 857 – 872. Week 13: Power Supply

Objectives: Students are expected to understand the working principles of each components and the coupling and functioning of the power supply. They also be able to calculate the output of the supply. Description: The student will be taught that power supply is a device that supplies electrical energy to one or more electric loads. The term is most commonly applied to devices that convert one form of electrical energy to another, though it may also refer to devices that convert another form of energy (e.g., mechanical, chemical, solar) to electrical energy. A regulated power supply is one that controls the output voltage or current to a specific value; the controlled value is held nearly constant despite variations in either load current or the voltage supplied by the power supply's energy source. Reading list: 1. Electricity and magnetism by S.G. Starling and A.J. Woodall (1962), William Clowes and Sons Ltd, London, Revised Edition, pp. 47 – 104, 305 – 384. 2. Fundamentals of Electricity and Magnetism by Arthur F.K. (1969) McGraw – Hill Inc. pp. 162 – 316, 382 – 431, 506 – 517.

3. David Halliday and Robert Resnick (1978), John Wiley and Sons Ltd., pp. 675 – 805, 857 – 872. Week 14 : Class Test and Revision Description: The students will be assessed on the whole course for 1 hour.

This week is scheduled for interactive sessions for: Discussion of problems arising from the topic treated in the previous weeks and the test.

Week 15 : Revision continues Activities of the previous week will be continued. Students should be well prepared for the examinations by the end of this week attempting questions. 1.

(a) State the expression for the magnetic field dB at a distance from a conductor that resulted from a current element idV according to BiotSavart law.



 o 4 

Idl

x r

 rn

idl



sin r 2



(b) Two long parallel wires A and B are 15cm apart and carry currents of 5A and 3A respectively. Find the force on a 2m length of wire B, if the currents are parallel. (c) Show that the magnetic field “B” at a distance x along the axis of conducting loop of radius R, carrying a current I is

Bx 

o I 2

R2 (x2



R2 )

(a)

State the expression for the magnetic field (dB) at a distance (r) from a conductor that resulted from a current element (idl), according to Biot – Savart law.

(b)

Two long parallel wires A and B are 15cm apart and carry currents of 5A and 3A respectively. Find the force on a 2m length of wire B, if

the currents are parallel. (Permeability of free space µ0 = 4π x 10-7 Tm/A, π = 3.142) (c)

(i)

Show that the magnetic field “B” at a distance x along the axis of conducting loop of radius R, carrying a current I is given by o I R2 Bx  3 2 ( x2  R2 ) 2

(ii)

Obtain the magnetic field at the centre of the loop, given that I = 5A and R = 0.02 m. (Permeability of free space µ0 = 4π x 10-7 Tm/A, π = 3.142)

3. (a) (b)

State Kirchhoff’s laws Find the current in each segment of the circuit I1, I2 and I3. R2 I1

B + R1

E1 -

R3 I2

Given that E1 = 10 V, E2 = 6 V, R1 = 2 Ω, R2 = 4 Ω, R3 = 1 Ω, and R4 = 3Ω. (c) Calculate the impedance of the circuit below

L = 25mH 10µF V = 100Sin 1000t R = 20 Ω

(a)

Write a short note on Faraday Law of Electromagnetic induction.

(b)

The armature of an AC generator rotates at a frequency of 60Hz and develops an emf of 120 V (root mean square value). The coil has an area of 2.0 x 10 - 3 m2 and consist of 400 turns. Find the magnitude of the magnetic field in which the coil rotates. (note: Erms = E0 /√2 ).

(c)

A galvanometer of resistance 20 Ohms gives a full scale deflection to a 5mA current. How would the galvanometer be modified to measure a

3A current? 5.

(a)

What is meant by transient current?

(b)

Consider a RC circuit in which the initial charge on the capacitor is q0 = EC. The switch is closed at time t = 0 and current I(t) starts to flow. Show that after time t, the charge on the capacitor and the current in the circuit are q (t) = q0 e-t/RC and I(t) = E/R e-t/RC respectively.

(c)

(i) Given R = 30 Ω , L = 100 H and the driving emf is 120 V in an RL series circuit. Calculate the time required for the current to reach half its equilibrium value. (ii) Obtain the time constant.

5. General Reading List: Reading list: 1. Electricity and magnetism by S.G. Starling and A.J. Woodall (1962), William Clowes and Sons Ltd, London, Revised Edition, pp. 47 – 104, 305 – 384. 2. Fundamentals of Electricity and Magnetism by Arthur F.K. (1969) McGraw – Hill Inc. pp. 162 – 316, 382 – 431, 506 – 517. 3. David Halliday and Robert Resnick (1978), John Wiley and Sons Ltd., pp. 675 – 805, 857 – 872.

6. LEGEND: Key for the Reading List: 1. 1 - Available in the University Library 2.

- Available in local bookshops

- Available on the Web

- Personal collection

- Departmental library