General physics 2 Electricity & Magnetism: Lecture 1

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General physics 2: Electricity & Magnetism products about Electric Charge and Field (Electric Charges; Coulomb’s Law; Electric Fields; Electric Field of a Continuous Charge Distribution; Motion of Charged Particles in a Uniform Electric Field).

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Nội dung Text: General physics 2 Electricity & Magnetism: Lecture 1

Ngac An Bang, Faculty of Physics, HUS GENERAL PHYSICS 2 Electricity & Magnetism 1
Ngac An Bang, Faculty of Physics, HUS Physics 2  Text book: Fundamentals of Physics, David Halliday et al., 8th Edition. Physics for Scientists and Engineers, Raymond A. Serway and John W. Jewett, 6th Edition.  Instructor: Dr. Ngac An Bang Faculty of Physics, Hanoi University of Science ngacanbang@hus.edu.vn  Homework: will be assigned and may be collected.  Quizzes and Exams:  There will be at least two (02) 15-minute quizzes.  There will be a mid-term exam and a final exam.  Grading policy:  Homework and Quizzes: 20 %  Midterm exam: 20 %  Final exam: 60 % 2
Ngac An Bang, Faculty of Physics, HUS Physics 2 Lecture 1 Electric Charge and Field  Electric Charges  Coulomb’s Law  Electric Fields  Electric Field of a Continuous Charge Distribution  Motion of Charged Particles in a Uniform Electric Field 3
Electric Charge and Field Ngac An Bang, Faculty of Physics, HUS Mother and daughter are both enjoying the effects of electrically charging their bodies. Each individual hair on their heads becomes charged and exerts a repulsive force on the other hairs, resulting in the “stand-up’’ hairdos that you see here. (Courtesy of Resonance Research Corporation) 4
Electric Charge and Field Ngac An Bang, Faculty of Physics, HUS Electric Charge Electric charge Some simple experiments demonstrate the existence of electric forces and charges  There are two types of charge. Convention dictates sign of charge:  Positive charge  Negative charge 5  Like charges repel, and opposite charges attract.
Electric Charge and Field Ngac An Bang, Faculty of Physics, HUS Electric Charge Quantization of Charge Charge is quantised  The smallest unit of “free” charge known in nature is the charge of an electron or proton, which has a magnitude of e = 1.602 x 10-19 C  Charge of any ordinary matter is quantized in integral multiples of the elementary charge e, Q = ± Ne.  An electron carries one unit of negative charge, -e,  While a proton carries one unit of positive charge, +e.  Note that although quarks (u, d, c, s, t, b) have smaller charge in comparison to electron or proton, they are not free particles. 6
Electric Charge and Field Ngac An Bang, Faculty of Physics, HUS Electric Charge Charge conservation A universal conservation law • In a closed system, the total amount of charge is conserved since charge can neither be created nor destroyed. • A charge can, however, be transferred from one body to another. • The β- reaction n → p + e + νe 0e = 1e -1e + 0e n(udd), p(uud) d → u + e + νe • Electron-positron annihilation e- + e+ → γ + γ • Pair production (γ-conversion) γ → e- + e+ 7
Electric Charge and Field Ngac An Bang, Faculty of Physics, HUS Electric Charge Some basic concepts  All materials acquire an electric charge  Neutral object: Total positive charge Q+= Total negative charge Q-.  Positively charged object: Q+ > Q-,  Negatively charged object: Q+ < Q-  In this part, we consider only two types of materials • Conductors: Electrical conductors are materials in which some of the electrons are free electrons that are not bound to atoms and can move relatively freely through the material; • Insulators: are materials in which electrons are bound to atoms and can not move freely through the material. 8
Electric Charge and Field Ngac An Bang, Faculty of Physics, HUS Charge Manipulation Charge transfer by contact Charging Objects By Induction 9
Electric Charge and Field Ngac An Bang, Faculty of Physics, HUS Coulomb’s Law Coulomb’s Law Consider a system of two point charges, q1 and q2, separated by a distance r in vacuum.  The force F12 exerted by q1 on q2 is given by Coulomb's law   q1q 2  q1q 2 r F12  k 2 r  k 2 r r r  The force F21 exerted by q2 on q1 is given by   F21   F12  The Coulomb constant k in SI units has the value 2 1 9 Nm k  8 .9875  10 4 0 C2  The constant ε0 is known as the permittivity of free space and has the value C2  0  8.854 2  10 -12 10 Nm 2
Electric Charge and Field Ngac An Bang, Faculty of Physics, HUS Coulomb’s Law Electric force  The electric force between charges q1and q2 is (a) repulsive if charges have same signs (b) attractive if charges have opposite signs  The electric force is a radial force, thus, a conservative force.  More than one force, Superposition principle is applied. 11
Electric Charge and Field Ngac An Bang, Faculty of Physics, HUS Coulomb’s Law Example 1 The electron and proton of a hydrogen atom are separated (on the average) by a distance of approximately 5.3 x10-11 m. Find and compare the magnitudes of the electric force and the gravitational force between the two particles. • From Coulomb’s law, we find that the magnitude of the electric force is e2 Nm 2 (1 . 6  10 19 C ) 2 8 FE  k 2  8 .8975  10 9 11  8 . 2  10 N r C (5 .3  10 m ) 2 2 • Using Newton’s law of universal gravitation we find that the magnitude of the gravitational force is me m p 11 Nm 2 (9 .1  10 31 kg )(1 .67  10 27 kg )  47 FG  G  6 . 67  10 11  3 . 6  10 N r 2 kg 2 (5 .3  10 m ) 2 • The ratio of them is F   E  2  10 39 FG Questions 1. Does the ratio γ depend on the distance r between the electron and the proton?. 12 2. What is the fundamental difference between the two forces?.
Electric Charge and Field Ngac An Bang, Faculty of Physics, HUS Coulomb’s Law Example 2 Find the force on the charge q3 assuming that q1 = -q2 = 6.0 μC, q3 = 3.0 μC, a = 2.0 x10-2 m  The total force F3 acting  on the charge  q3 is F3  F13  F23  The electric force F13 can be calculated as   1 q1q 3 r13 1 q1q 3 F13   rˆ13 4 0 r132 r13 4 0 r132      1 q1q 3   1 q1q 3 2   F13  cos  .i  sin  . j  i  j 4 0 2 a 2 4 0 a 2 4  The electric force F23 can be calculated as     1 q 2 q 3 r23 1 q 2 q3 1 q1 q 3  F23   rˆ23  i 4 0 r232 r23 4 0 r232 4 0 a 2  Finally,     2   1 q1q 3 2 F3  F13  F23     1i  j 4 0 a 2  4  4  13
Electric Charge and Field Ngac An Bang, Faculty of Physics, HUS Coulomb’s Law Example 2 Find the force on the charge q3 assuming that q1 = -q2 = 6.0 μC, q3 = 3.0 μC, a = 2.0 x10-2 m  The total force F3 acting on the charge q3 is    1 q1q 3  2  2  F3  F13  F23   2   1  i  j 4 0 a  4  4   The magnitude F3 is 1/ 2  1 q1q 3  2 2   2  2  F3    1       3 .0 N 4 0 a  4 2       4    Angle ϕ can be calculated as F3 y 2 /4 tan       151 .3 0 F3 x  2     4  1 14  
Electric Charge and Field Ngac An Bang, Faculty of Physics, HUS Electric Field Defining the electric field  What is the mechanism by which one particle can exert a force on another across the empty space between particles?  Suppose a charge is suddenly moved. Does the force exerted on a second particle some distance r away change instantaneously?  A charge produces an electric field everywhere in space.  The force is exerted by the field at the position of the second charge.  The field propagates through space at the speed of light.  It’s a vector field. 15
Electric Charge and Field Ngac An Bang, Faculty of Physics, HUS Electric Field Defining the electric field  The electric  field vector E at a point in space is defined as the electric force F acting on a positive test charge q0 placed at that point divided by the test charge:   F E q0 16 The SI unit of the electric field is N/C
Electric Charge and Field Ngac An Bang, Faculty of Physics, HUS Electric Field Electric field of a point charge   An electric charge q produces an electric field E everywhere.  If we put a positive test charge q0 at any point P a distance r away from  the point charge q, the electrostatic force F exerts on a test charge is  1 qq 0 r F   4 0 r 2 r  The electric field E created by the charge q at point P is    F 1 q r E  q 0 4 0 r 2 r 17
Electric Charge and Field Ngac An Bang, Faculty of Physics, HUS Electric Field Field lines 1.The electric field vector is tangent to the electric field line at each point 2.Field lines point away from positive charges and terminate on negative charge 3.Field lines never cross each other 4. The number of lines per unit area through a surface perpendicular to the lines is proportional to the magnitude of the electric field in a given region. 18
Electric Charge and Field Ngac An Bang, Faculty of Physics, HUS Electric Field Superposition principle At any point P, the total electric field due to a group of source charges equals the vector sum of the electric fields of all the charges.  If we place a positive test charge q0 near n point charges q1, q2, q3 …, qn, then the net force F0 from n point charges acting on the test charge is      n  F0  F10  F20  F30  ...  Fn 0   Fi 0 i 1  By definition, the electric field E at the position of the test charge is n   F0   Fi 0 n  Fi 0 n  E  i 1    Ei q0 q0 i 1 q 0 i 1 19
Electric Charge and Field Ngac An Bang, Faculty of Physics, HUS Electric Field Electric dipole An electric dipole is defined as a positive charge +q and a negative charge -q separated by a distance d. For the dipole shown in this figure, 1. Find the electric field E at P due to the dipole, where P is a distance y from the origin. 2. Find the electric field E at Q due to the dipole, where Q is a distance x from the origin. 20