Electricity and Magnetism 2 By Henri RASOLONDRAMANITRA African Virtual university Université Virtuelle Africaine Universidade Virtual Africana African Virtual University NOTICE This document is published under the conditions of the Creative Commons http://en.wikipedia.org/wiki/Creative_Commons Attribution http://creativecommons.org/licenses/by/2.5/ License (abbreviated “cc-by”), Version 2.5. African Virtual University Table of conTenTs I. Electricity and Magnetism 2 __________________________________ 3 II. Prerequisite Course or knowledge _____________________________ 3 III. Time ____________________________________________________ 3 IV. Material __________________________________________________ 3 V. Module Rationale __________________________________________ 4 VI. Content __________________________________________________ 4 6.1 Overview ______________________________________________ 4 6.2 Outline________________________________________________ 5 6.3 Graphic Organizer _______________________________________ 5 VII. General Objective(s) ________________________________________ 6 VIII. Specific Learning Objectives __________________________________ 7 IX. Teaching and Learning Activities _______________________________ 9 X. Learning Activities _________________________________________ 20 XI. Key Concepts (Glossary) ___________________________________ 161 XII. Compulsory Readings _____________________________________ 164 XIII. Useful Links ____________________________________________ 167 XIV. Synthesis of the Module ___________________________________ 189 XV. Summative Evaluation _____________________________________ 190 XVI. References _____________________________________________ 262 XVII. Main Author of the Module _________________________________ 265 African Virtual University I. Electricity and Magnetism 2 By Dr. Henri Rasolondramanitra II. Prerequisite course or knowledge In order to be able to complete this course, you must have successfully passed the magnitude Electricityand Magnetism 1 and you must have a clear understanding of the following notions: Ohm’s Law; Kirchoff’s laws; Effect of an electric field on a charged particle Effect of a magnetic field on a moving charged particle Magnetic flux Ampere’s theorems III. Time You will need approximately 120 hours to complete the entire course, divided into the following sections: 1. Circuits in alternative current- Bridges in alternative current 30 hours 2. Magnetic fields and charged particles – Inductance 30 hours 3. Magnetic properties of matter 30 hours 4. Maxwell’s equations – electromagnetic waves 30 hours IV. Material You will need the following materials: Computer with internet connection, printer, Microsoft office, MathType software. African Virtual University V. Module Rationale Electromagnetism is a part of physics of which the applications in ordinary, day-to-day life are countless and fascinating. Among just a few, we can mention television, radio and mobile telephone systems which use electromagnetic waves in order to function. This magnitude will help the learner acquire a few basic and indispensable notions in order to understand this field better. In addition, it will allow the learner to reinforce his/her pedagogical competencies with a view to teaching this discipline. VI. content 6.1 Overview The first part of this magnitude will examine alternative powered circuits, circuits which display diverse combinations of resistance, inductance and capacity. The second part will examine the momentum of charged particles in both electric and magnetic fields. We will describe and explain J.J. Thompson’s experiment, the Hall effect and the principle of accelerating particles such as cyclotrons and synchrotrons. Next we will study the electromagnetic induction phenomenon, Lenz’s law, auto- and mutual induction phenomena and their resulting applications. The third section will describe and analyze the properties of the three classes of magnetic substances: the paramagnetic, the ferromagnetic and the diamagnetic. The last part of the magnitude explains the four fundamental equations (Maxwell’s equations) which underlie elec- tromagnetism and examine electromagnetic waves, their polarization and the energy they transport. African Virtual University 6.2 Outline The magnitude consists of four parts which progress as follows: 1. Circuits in alternating current – Bridges in alternating current 2. Magnetic fields and charged particles – Inductance 3. Magnetic properties of matter 4. Maxwell’s equations – electromagnetic waves 6.3 Graphic Organizer Electricity and magnetism 2 Circuits and bridges in alternating current Magnetic fields and charged particles Inductance Magnetic properties of matter Maxwell’s equations Eletromagnetic waves African Virtual University VII. General objectives The learner should have an understanding of the following: - The phase relation between the tension applied to the limits of a circuit in alternative voltage and its current - The notion of impedance - The resonance phenomenon in an RLC circuit series - The Hall effect - The principle of a cyclotron - Lenz’s law - The auto-induction phenomenon - The mutual induction phenomenon - The magnetic properties of matter - Maxwell’s equations - The phenomenon of energy transmission through an electromagnetic wave - The notion of polarization of an electromagnetic wave African Virtual University VIII. specific learning objectives Unit Learning Objective 1. Circuits in - Determine the outcome of two or more vectors Alternative current - - Establish the phase difference between tension Bridges in Alternative current according to Fresnel’s construction 30 hours and current in a circuit with resistance - Establish the phase difference between tension and current in a coiled circuit - Establish the phase difference between tension and current in a circuit with condenser - Establish the phase difference between tension and current in an RLC circuit - Calculate the impedance of an RLC circuit - Calculate the quality factor of an RLC circuit series - Calculate the band-width of an RLC circuit series - Calculate the frequency resonance - Distinguish efficient and instant values of the tension and the intensity of the electric current - Calculate the instant value of the intensity of a current passing through a circuit - Calculate the instant value of the tension at the limits of a circuit - Recall the relation between the efficient value of the intensity and amplitude of the current passing through a circuit - Recall the relation between the efficient value and the amplitude of tension at the limits of a circuit 2. Magnetic field - Recall Lenz’s law and charged particle - Apply Lenz’s law - Inductance - Describe the Hall effect 30 hours - Interpret the Hall effect - Determine the relation e m - Calculate the radius of a charge carrier’s trajectory in a cyclotron - Calculate the inductance of a circuit - Calculate the mutual coefficient induction of two circuits African Virtual University 3. Magnetic properties - Describe the phenomenon of paramagnetism Of matter: - Interpret the phenomenon of paramagnetism 30 hours - Describe the phenomenon of diamagnetism - Interpret the phenomenon of diamagnetism - Describe the phenomenon of ferromagnetism - Interpret the phenomenon of ferromagnetism - Recall the relationship between a magnetic induction field’s vectors, magnetic activity and magnetization - Recall the Hysterisis phenomenon - Calculate the magnetization of a magnetic substance 4. Maxwell’s Equations - - Apply Maxwell’s equations Electromagnetic waves: - Determine the polarization of a plane electro- 30 hours magnetic wave - Determine the Poynting vector associated with a plane electromagnetic wave - Determine the energy density of a plane electro- magnetic wave - Determine the intensity of a plane electro- Magnetic wave - Determine the radiation pressure of electro- magnetic wave African Virtual University IX. Teaching and learning activities Pre-Assesment Evaluation Prerequisite Testing Electricityand magnetism 2 Learning Objective : This test will allow you to verify your knowledge of previous material in order to be able to complete this magnitude. It is therefore compulsory for all learners. Questions Check the appropriate box in all of the following Exercise 1 Consider the circuit below : The intensity of the current I which passes through the circuit and the difference in potential of VAB at the limits of R1 are : 1 : I = 2A and VAB = 6 V 2 : I = 1A and VAB = 3 V 3 : I = 1,33A and VAB = 3,99 V African Virtual University 0 Exercise 2 : Consider the circuit below: The difference in potential VAB at the limits of resistance R2 and the intensity of the current I2 which passes through this resistance are : 1 : VAB = 2 V and I2 = 12A 2 : VAB = 4 V and I2 = 24A 3 : VAB = 12 V and I2 = 2A Exercise 3 : Consider the circuit below: G1 and G2 are two generators with f.e.m. ε1 and ε2. G1AG2BG1 are linked as fol- lows: G A G B G : The application of Kirchhoff’s law in this link results 1 → → 2 → → 1 in the following 1 : - = R I + R I ε1 ε2 1 1 3 3 2 : + = R I + R I ε1 ε2 1 1 3 3 3 : - = R I + R I ε2 ε1 1 1 3 3 African Virtual University 11 Exercise 4 → Consider the figure above. An electron with a horizontal speed V penetrates a region → → comprised of an electric field E and a magnetic field B. B is perpendicular to the → direction of V as the figure shows. If the electron does not deviate from its initial → trajectory, E will travel according to the following: 1 : Positively along the y axis 2 : Negatively