01. Introduction and Electric Field I

Transcription

1 University of Rhode Island PHY 204: lementary Physics II Physics Course Materials Introduction and lectric Field I Gerhard Müller University of Rhode Island, gmuller@uri.edu Creative Commons License This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License. Follow this and additional works at: Abstract Part one of course materials for lementary Physics II (PHY 204), taught by Gerhard Müller at the University of Rhode Island. Documents will be updated periodically as more entries become presentable. Some of the slides contain figures from the textbook, Paul A. Tipler and Gene Mosca. Physics for Scientists and ngineers, 5 th /6 th editions. The copyright to these figures is owned by W.H. Freeman. We acknowledge permission from W.H. Freeman to use them on this course web page. The textbook figures are not to be used or copied for any purpose outside this class without direct permission from W.H. Freeman. Recommended Citation Müller, Gerhard, "01. Introduction and lectric Field I" (2015). PHY 204: lementary Physics II. Paper This Course Material is brought to you for free and open access by the Physics Course Materials at DigitalCommons@URI. It has been accepted for inclusion in PHY 204: lementary Physics II by an authorized administrator of DigitalCommons@URI. For more information, please contact digitalcommons@etal.uri.edu.

2 PHY204: lementary Physics II Welcome to PHY204. Instructor: Gerhard Muller, 320D ast Hall. Syllabus is posted online. Check for online updates. Course webpage: Register (separately) for lecture, lab, and recitation. Lecture slides are available online. Come to class regularly and be on time. arn extra credit by participating in daily quiz. Bring your textbook and your calculator. xams: 3 unit exams (in class) and final exam. Closed book, calculator needed, one sheet of notes permitted. xam topics will be reviewed in class. Homework: Online submission via WebAssign. Check due dates online. PHY274 Laboratory: Semester schedule on syllabus. Purchase lab notebook and lab manual. PHY274 Recitation: Semester schedule on syllabus. Bring textbook and calculator. 1/9/2015 [asl1 1/30]

3 Mechanics Kinematics: position: r(t) = Z velocity: v(t) = d r dt = v(t) dt Z a(t) dt acceleration: a(t) = d v dt = d2 r dt 2 Dynamics: cause and effect: F = m a Modes of motion: translation, rotation Conservation laws: energy, momentum, angular momentum ffective forces: elastic, contact, friction,... Fundamental forces: gravitational, electric, magnetic,... 1/9/2015 [tsl1 2/30]

4 lectricity and Magnetism Particles generate fields: Massive particle generates gravitational field. Charged particle generates electric field. Moving charged particle generates magnetic field. Fields exert force on particles: Gravitational field exerts force on massive particle. lectric field exerts force on charged particle. Magnetic field exerts force on moving charged particle. Dynamics: Cause and effect between particles and fields and among fields. nergy and momentum: Particles carry energy (kinetic, potential) and momentum. Fields carry energy (electric, magnetic) and momentum. 1/9/2015 [tsl2 3/30]

5 Atomic Structure of Matter Periodic table: 100 elements. Building blocks of atoms: fundamental particles. SI unit of charge: 1C (Coulomb). particle charge mass lementary charge: e = C. electron q e = e m e = kg proton q p = +e m p = kg neutron q n = 0 m n = kg Atomic nuclei (protons, neutron) have a radius of 1fm = m. Atomic electron shells have a radius of 1Å = m. Atoms are electrically neutral (equal numbers of electrons and protons). Ions: atoms with one or several electrons added or removed. Isotopes: atoms differing in the number of neutrons. Positively (negatively) charged objects have a deficiency (surplus) of electrons. 1/9/2015 [tsl3 4/30]

6 Periodic Table of lements 1/9/2015 [tsl368 5/30]

7 Charged Insulators and Conductors 1/9/2015 [tsl369 6/30]

8 Charged Insulators and Conductors 1/9/2015 [tsl369 6/30]

9 Coulomb s Law (1) lectrostatic force between two charged particles: F = 1 q 1 q 2 4πǫ 0 r 2 = k q 1q 2 r 2 Permittivity constant: ǫ 0 = C 2 N 1 m 2 Coulomb constant: k = Nm 2 C q r F 21 F q 1 2 Action-reaction pair of forces: F21 = F 12. 1/9/2015 [tsl4 7/30]

10 Coulomb s Law (1) lectrostatic force between two charged particles: F = 1 q 1 q 2 4πǫ 0 r 2 = k q 1q 2 r 2 Permittivity constant: ǫ 0 = C 2 N 1 m 2 Coulomb constant: k = Nm 2 C q r F 21 F q 1 2 Action-reaction pair of forces: F21 = F 12. Newton s law of gravitation Gravitational force between two massive particles: F = G m 1m 2 r 2 r F 21 F m 12 1 m 2 Gravitational constant: G = Nm 2 kg 2 1/9/2015 [tsl4 7/30]

11 Coulomb s Law (2) Coulomb s law for electrostatic force in vector form: F 12 = k q 1q 2 r 2 12 ˆr 12, r 12. = r2 r 1, ˆr 12. = r 12 r 12. 1/9/2015 [tsl370 8/30]

12 Coulomb s Law (2) Coulomb s law for electrostatic force in vector form: F 12 = k q 1q 2 r 2 12 ˆr 12, r 12. = r2 r 1, ˆr 12. = r 12 r 12. lectric force in hydrogen atom: Average distance: r = m. lementary charge: e = C. F = k q 1q 2 r 2 = ( Nm 2 /C 2 )( C) 2 ( m) 2 = N. 1/9/2015 [tsl370 8/30]

13 Coulomb Force in One Dimension (1) Find net force on charge q 0 due to charges q 1 and q 2. Consider x-component of force. F 0 = +k q 1q 0 (3.5m) 2 k q 2q 0 (1.5m) 2 = N N = N. Find net force on charge q 2 due to charges q 1 and q 0. F 2 = k q 1q 2 (2.0m) 2 + k q 2q 0 (1.5m) 2 = N N = N. 1/9/2015 [tsl5 9/30]

14 Coulomb Force in One Dimension (2) Three particles with charges of magnitude 1C are positioned on a straight line with two equal spacings. q q q (a) Find the direction (left/right) of the net forces F 1, F 2, F 3 on each particle. (b) Which force is the strongest and which force is the weakest? 1/9/2015 [tsl6 10/30]

15 Coulomb Force in One Dimension (3) Four point charges equal magnitude are lined up in three different configurations. The Coulomb force between nearest neighbors is 4N. (a) (b) (c) Find direction and magnitude of the net force experienced by the green particle in each configuration. 1/9/2015 [tsl7 11/30]

16 Coulomb Force in One Dimension (4) Three charged particles are positioned along a straight line with two equal spacings. The net Coulomb force on charge q 3 happens to vanish. d d F = 0 3 q =? q =1µ C q = 2 µ C What is the value of q 1? 1/9/2015 [tsl8 12/30]

17 Coulomb Force in One Dimension (5) How are the forces F 1 and F 2 in (a) affected by the changes made in (b) and (c)? (a) (b) (c) F q 1 = +1C q 2 = +1C 1 2 q 1 = +1C q 2 = +2C 1m 1m q 1 = +1C q 2 = +2C F What changes if the charge q 2 is made negative? 1/9/2015 [tsl347 13/30]

18 Coulomb Force in Two Dimensions (1a) Find the magnitude and direction of the resultant force on charge q 0. Magnitude of individual forces: F 1,0 = k q 1q 0 r 2 1,0 = N, F 2,0 = k q 2q 0 r 2 2,0 = N. Components of individual forces: F x 1,0 = F 1,0 cos 45, F y 1,0 = F 1,0 sin45, F x 2,0 = 0, F y 2,0 = F 2,0. 1/9/2015 [tsl9 14/30]

19 Coulomb Force in Two Dimensions (1b) Components of resultant force: F x = F x 1,0 + F x 2,0 = N, F y = F y 1,0 + F y 2,0 = N. Magnitude of resultant force: F = q F 2 x + F2 y = N. Direction of resultant force: θ = arctan (F y /F x ) = /9/2015 [tsl325 15/30]

20 Coulomb Force in Two Dimensions (2) The unknwon point charges q 1, q 2 exert a force F 0 = 2N on the known point charge q 0 = 1nC. This force is directed in the positive y-direction as shown. Determine first whether q 1, q 2 are positive or negative. Then determine the values of the two point charges. y 3m q 2 F 0 3m x q 0 q 1 1/9/2015 [tsl10 16/30]

21 Coulomb Force in Two Dimensions (2) The unknwon point charges q 1, q 2 exert a force F 0 = 2N on the known point charge q 0 = 1nC. This force is directed in the positive y-direction as shown. Determine first whether q 1, q 2 are positive or negative. Then determine the values of the two point charges. y 3m q 2 F 0 3m F 10 F 2 0 q 0 q 1 x 1/9/2015 [tsl10 16/30]

22 Coulomb Force in Two Dimensions (3) Point charges of equal magnitude are positioned at the corners of an equilateral triangle. q = 1nC 1 q = 1nC 2 q = 1nC 3 Copy this configuration and indicate by arrows the direction of the resultant force on each point charge. Which point charge experiences the strongest force? 1/9/2015 [tsl11 17/30]

23 Coulomb Force in Two Dimensions (4) Point charges of equal magnitude are positioned at the corners of a square. Copy this configuration and indicate by arrows the direction of the resultant force on each point charge. If the force between nearest-neighbor charges is 1N, what is the strength of the resultant force on each charge? 1/9/2015 [tsl12 18/30]

24 Coulomb Force in Two Dimensions (5) Two identical small charged spheres, each having a mass m = 30g, hang in equilibrium at an anlge of θ = 5 from the vertical. The length of the strings is L = 15cm. L θ θ L q q Identify all forces acting on each sphere. Find the magnitude of the charge q on each sphere. 1/9/2015 [tsl13 19/30]

25 Coulomb Force in Two Dimensions (5) Two identical small charged spheres, each having a mass m = 30g, hang in equilibrium at an anlge of θ = 5 from the vertical. The length of the strings is L = 15cm. T L θ θ L F e q q mg Identify all forces acting on each sphere. Find the magnitude of the charge q on each sphere. 1/9/2015 [tsl13 19/30]

26 lectric Field of a Point Charge electric charge generates electric field exerts force locally electric charge exerts force over distance (1) lectric field generated by point charge q: = k q r 2 ˆr (2) Force F 1 exerted by field on point charge q 1 : F1 = q 1 (1+2) Force F 1 exerted by charge q on charge q 1 : F 1 = k qq 1 r 2 ˆr (static conditions) ǫ 0 = C 2 N 1 m 2 k = 1 4πǫ 0 = Nm 2 C 2 q + source point r r field point ^r field point ^r 1/9/2015 [tsl14 20/30]

27 Superposition Principle for lectric Field lectric field on line connecting two point charges: + q q lectric field of point charges in plane: + q q /9/2015 [tsl15 21/30]

28 Vector Field and lectric Field Lines The electric field is a vector field: ( r) = (x, y, z) = x (x, y, z)î + y (x, y, z)ĵ + z (x, y, z)ˆk lectric field lines: graphical representation of vector field. Properties of electric field lines (electrostatics): lectric field lines begin at positive charges or at infinity. lectric field lines end at negative charges or at infinity. The direction of is tangential to the field line going through the field point. lectric field lines bunched together indicate a strong field. lectric field lines far apart indicate a weak field. Field lines do not intersect. 1/9/2015 [tsl22 22/30]

29 lectric Field on Line Connecting Point Charges (1) Consider the x-component of the electric field. lectric field at point P 1 : = = kq 1 (7m) 2 + kq 2 = 1.47N/C N/C = 13.5N/C. (3m) 2 lectric field at point P 2 : = = kq 1 (3m) 2 kq 2 = 7.99N/C 108N/C = 100N/C. (1m) 2 q = +8nC 1 q =+12nC P 2 2 P x [m] 1/9/2015 [tsl19 23/30]

30 lectric Field on Line Connecting Point Charges (2) Four particles with charges of equal magnitude are positioned on a horizontal line in six different configurations. (a) (b) (c) (d) (e) (f) Determine for each configuration the direction of the resultant electric field (left/right/zero) at the location indicated by. 1/9/2015 [tsl16 24/30]

31 lectric Field on Line Connecting Point Charges (3) Is the unknown charge positive or negative? What is the value of the unknown charge? (a) 2m +? 9nC 3m =0 (b)? 2m 3m =0 + 9nC 1/9/2015 [tsl17 25/30]

32 lectric Field of Point Charges in Plane (1) Determine magnitude of 1 and 2 and identify directions in plane: 1 = k q 1 (3m) 2 =7.99N/C, 2 = k q 2 (5m) 2 =4.32N/C. 1 Determine x- and y-components of 1 and 2 and of the resultant field : 2 3 θ x 1 = 0, y 1 = 7.99N/C; 2 x 2 = 3.46N/C, x = 3.46N/C, y 2 = 2.59N/C; y = 10.6N/C. 1 q = +8nC 1 q =+12nC 2 Determine magnitude and direction of : = q 2 x + 2 y = 11.2N/C, θ = arctan y x «= [m] x 1/9/2015 [tsl18 26/30]

33 lectric Field of Point Charges in Plane (2) (a) Find the electric charge q o 1m 1m + q = 3nC 1 q =? 2 θ =? 1m (b) Find the angle θ. 1m q = 2nC 1 q = 4nC 2 1/9/2015 [tsl20 27/30]

34 lectric Field of Point Charges in Plane (3) Two point charges, one known and the other unknown, produce a horizontal electric field as shown. What is the value of the unknown charge? 5m 5m q =? 1nC 1/9/2015 [tsl21 28/30]

35 lectric Field of Point Charges in Plane (5) Find magnitude and direction of the resultant electric field at point P. 1 = k q 1 8m 2 = 3.38N/C. 2 = k q 2 4m 2 = 6.75N/C. 3 = k q 3 8m 2 = 3.38N/C. x = 1 cos cos45 = 4.78 N/C. y = 2 = 6.75 N/C. q = x y = 8.27 N/C. 2 P 2m 3 1 y θ x tan θ = y x = θ = arctan 1.41 = q = +3nC 1 2m q = +3nC 2 2m q = 3nC 3 x 1/9/2015 [tsl371 29/30]

36 Intermediate xam I: Problem #1 (Spring 05) The electric field generated by the two point charges, 3nC and q 1 (unknown), has the direction shown. (a) Find the magnitude of. (b) Find the value of q 1. y 45 o 4m q 1 x 2m 3nC 1/9/2015 [tsl331 30/30]

37 Intermediate xam I: Problem #1 (Spring 05) The electric field generated by the two point charges, 3nC and q 1 (unknown), has the direction shown. (a) Find the magnitude of. (b) Find the value of q 1. y Solution: (a) y = k 3nC (2m) 2 = 6.75N/C, x = y, q = x y = 9.55N/C. 2m 3nC 45 o 4m q 1 x 1/9/2015 [tsl331 30/30]

38 Intermediate xam I: Problem #1 (Spring 05) The electric field generated by the two point charges, 3nC and q 1 (unknown), has the direction shown. (a) Find the magnitude of. (b) Find the value of q 1. y Solution: (a) y = k 3nC (2m) 2 = 6.75N/C, x = y, q = x y = 9.55N/C. (b) x = k ( q 1) (4m) 2, q 1 = (6.75N/C)(16m2 ) k = 12nC. 2m 3nC 45 o 4m q 1 x 1/9/2015 [tsl331 30/30]