05. Electric Potential I

Size: px
Start display at page:

Download "05. Electric Potential I"

Transcription

1 University of Rhode Island PHY 204: Elementary Physics II Physics Course Materials Electric Potential 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 five of course materials for Elementary 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 Engineers, 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, "05. Electric Potential I" (2015). PHY 204: Elementary 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: Elementary Physics II by an authorized administrator of DigitalCommons@URI. For more information, please contact digitalcommons@etal.uri.edu.

2 Work and Energy Consider a block of mass m moving along the x-axis. Conservative force acting on block: F = F(x) Work done by F(x) on block: W if = Kinetic energy of block: K = 1 2 mv2 Potential energy of block: U(x) = Z xf x i Z x F(x)dx x 0 F(x)dx F(x) = du dx Transformation of energy: K K f K i, U U f U i Total mechanical energy: E = K + U = const K + U = 0 Work-energy relation: W if = K = U v i v f m F(x ) i m F(x ) f x x i x f 2/9/2015 [tsl67 1/21]

3 Conservative Forces in Mechanics Conservative forces familiar from mechanics: Elastic force: F(x) = kx U(x) = Gravitational force (locally): F(y) = mg U(y) = Z y Z x x 0 ( kx)dx = 1 2 kx2 (x 0 = 0). y 0 ( mg)dy = mgy (y 0 = 0). Gravitational force (globally): F(r) = G mm E r 2 U(r) = Z r r 0 G mm E r 2 dr = G mm E r (r 0 = ). Potential energy depends on integration constant. Integration constant determines reference position where U = 0: x = x 0, y = y 0, r = r 0. 2/9/2015 [tsl68 2/21]

4 Work and Potential Energy in 3D Space Consider a particle acted on by a force F as it moves along a specific path in 3D space. Force: F = F x î + F y ĵ + F zˆk Displacement: d s = dxî + dyĵ + dzˆk Work: W if = Z rf Potential energy: U( r) = Z xf Z yf F d s = F x dx + F y dy + r i x i y i Z zf z i Z r Z x Z y F z dz F d s = F x dx F y dy r 0 x 0 y 0 z Z z z 0 F z dz Note: The work done by a conservative force is pathindependent. f F ds y x i 2/9/2015 [tsl69 3/21]

5 Potential Energy of Charged Particle in Uniform Electric Field Electrostatic force: F = qeĵ (conservative) Displacement: d s = dxî + dyĵ Work: W if = Z f i F d s = Potential energy: U = Z y Electric potential: V (y) = Ey 0 Z yf y i ( qe)dy = qe(y f y i ) ( qe)dy = qey y y i E ds i q F = qe y f f x 2/9/2015 [tsl70 4/21]

6 Potential Energy of Charged Particle in Coulomb Field Electrostatic force: F = kqq r 2 ˆr Displacement: d s = d r + d s, (conservative) d r = drˆr Z f Z f ˆr d s Work: W if = F d s = kqq i i r 2 = kqq» = kqq 1 rf» 1 = kqq 1 r r i r f r i Potential energy: U = Z r Fdr = kqq Z r dr Z rf r i r 2 = k qq r dr r 2 Electric potential: V (r) = kq r dr q ds f i r r f. r i + Q 2/9/2015 [tsl71 5/21]

7 Attributes of Space and of Charged Particles planar source point source SI unit electric field E = Ex î E = kq r 2 ˆr electric potential V = E x x V = kq r electric force F = qe = qex î F = qe kqq = r 2 ˆr electric potential energy U = qv = qe x x U = qv = kqq r [N/C]=[V/m] [V]=[J/C] [N] [J] Electric field E is present at points in space. Points in space are at electric potential V. Charged particles experience electric force F = q E. Charged particles have electric potential energy U = qv. 2/9/2015 [tsl447 6/21]

8 Equipotential Surfaces and Field Lines Definition: V ( r) = const on equipotential surface. Potential energy U( r) = const for point charge q on equipotential surface. The surface of a conductor at equilibrium is an equipotential surface. Electric field vectors E( r) (tangents to field lines) are perpendicular to equipotential surface. Electrostatic force F = q E( r) does zero work on point charge q moving on equipotential surface. The electric field E( r) exerts a force on a positive (negative) point charge q in the direction of steepest potential drop (rise). When a positive (negative) point charge q moves from a region of high potential to a region of low potential, the electric field does positive (negative) work on it. In the process, the potential energy decreases (increases). 2/9/2015 [tsl80 7/21]

9 Topographic Maps Gravitation Electricity 2/9/2015 [tsl421 8/21]

10 Electric Potential and Potential Energy: Application (1) Consider a point charge Q = 2µC fixed at position x = 0. A particle with mass m = 2g and charge q = 0.1µC is launched at position x 1 = 10cm with velocity v 1 = 12m/s. (fixed) Q = 2µC x = 0 m = 2g q = 0.1µC v 1 x 1= 10cm x 2= 20cm Find the velocity v 2 of the particle when it is at position x 2 = 20cm. 2/9/2015 [tsl73 9/21]

11 Electric Potential and Potential Energy: Application (2) Electric potential at point P 1 : V = kq m + kq m Electric potential at point P 2 : V = kq kq m = 1125V V = 2250V. = 750V + 450V = 1200V. 2/9/2015 [tsl74 10/21]

12 Electric Potential and Potential Energy: Application (3) Point charges q 1 = 5.0µC and q 2 = +2.0µC are positioned at two corners of a rectangle as shown. q = 5.0µC 1 15cm 5cm A B q =+2.0µC 2 (a) Find the electric potential at the corners A and B. (b) Find the electric field at point B. (c) How much work is required to move a point charge q 3 = +3µC from B to A? 2/9/2015 [tsl75 11/21]

13 Electric Potential and Potential Energy: Application (4) A positive point charge q is positioned in the electric field of a negative point charge Q. (1) Q = 10µC 2m q = +5µC (2) Q = 10µC 1m q = +1µC (a) In which configuration is the charge q positioned in the stronger electric field? (b) In which configuration does the charge q experience the stronger force? (c) In which configuration is the charge q positioned at the higher electric potential? (d) In which configuration does the charge q have the higher potential energy? 2/9/2015 [tsl76 12/21]

14 Electric Potential and Potential Energy: Application (5) An electron and a proton are released from rest midway between oppositely charged plates E (a) Name the particle(s) which move(s) from high to low electric potential. (b) Name the particle(s) whose electric potential energy decrease(s). (c) Name the particle(s) which hit(s) the plate in the shortest time. (d) Name the particle(s) which reach(es) the highest kinetic energy before impact. 2/9/2015 [tsl77 13/21]

15 Electric Potential and Potential Energy: Application (6) Three protons are projected from x = 0 with equal initial speed v 0 in different directions. They all experience the force of a uniform horizontal electric field E. Ultimately, they all hit the vertical screen at x = L. p1 p2 E p3 x = 0 x = L x (a) Which proton travels the longest time? (b) Which proton travels the longest path? (c) Which particle has the highest speed when it hits the screen? Two of the questions are easy, one is hard. 2/9/2015 [tsl78 14/21]

16 Electric Potential and Potential Energy: Application (7) Consider a region of nonuniform electric field. Charged particles 1 and 2 start moving from rest at point A in opposite directions along the paths shown. C 2 q = 1C 2 A V = 17V A 1 q = +3C 1 B V = 11V B From the information given in the figure... (a) find the kinetic energy K 1 of particle 1 when it arrives at point B, (b) find the electric potential V C at point C if we know that particle 2 arrives there with kinetic energy K 2 = 8J. 2/9/2015 [tsl79 15/21]

17 Electric Potential and Potential Energy: Application (8) (a) Is the electric potential at points P 1, P 2 positive or negative or zero? (b) Is the potential energy of a negatively charged particle at points P 1, P 2 positive or negative or zero? (c) Is the electric field at points P 1, P 2 directed left or right or is it zero? (d) Is the force on a negatively charged particle at points P 1 and P 2 directed left or right or is it zero? 2nC P 1 4nC 3cm 6cm 2nC P 2 4nC 3cm 6cm 2/9/2015 [tsl83 16/21]

18 Electric Potential and Potential Energy: Application (9) Consider four point charges of equal magnitude positioned at the corners of a square as shown. Answer the following questions for points A, B, C. (1) Which point is at the highest electric potential? (2) Which point is at the lowest electric potential? (3) At which point is the electric field the strongest? (4) At which point is the electric field the weakest? +q A +q B q C q 2/9/2015 [tsl84 17/21]

19 Electric Potential and Potential Energy: Application (10) The charged particles 1 and 2 move between the charged conducting plates A and B in opposite directions. From the information given in the figure... (a) find the kinetic energy K 1B of particle 1, (b) find the charge q 2 of particle 2, (c) find the direction and magnitude of the electric field E between the plates. K1A =3µJ q 1 = 2µC 1 K 1B =? K 2A = 10µ J V = 19V A q 2 =? 2 2m V = 13V B K 2B = 4µ J 2/9/2015 [tsl90 18/21]

20 Intermediate Exam I: Problem #2 (Spring 05) Consider a point charge Q = 5nC fixed at position x = 0. (a) Find the electric potential V 1 at position x 1 = 3m and the electric potiential V 2 at position x 2 =. (b) If a charged particle (q = 4nC, m = 1.5ng) is released from rest at x 1, what are its kinetic energy K 2 and its velocity v 2 when it reaches position x 2? Q = 5nC x = 0 x 1= 3m x 2= 2/9/2015 [tsl332 19/21]

21 Intermediate Exam I: Problem #2 (Spring 05) Consider a point charge Q = 5nC fixed at position x = 0. (a) Find the electric potential V 1 at position x 1 = 3m and the electric potiential V 2 at position x 2 =. (b) If a charged particle (q = 4nC, m = 1.5ng) is released from rest at x 1, what are its kinetic energy K 2 and its velocity v 2 when it reaches position x 2? Q = 5nC Solution: x = 0 x 1= 3m x 2= (a) V 1 = k Q x 1 = 15V, V 2 = k Q x 2 = 7.5V. 2/9/2015 [tsl332 19/21]

22 Intermediate Exam I: Problem #2 (Spring 05) Consider a point charge Q = 5nC fixed at position x = 0. (a) Find the electric potential V 1 at position x 1 = 3m and the electric potiential V 2 at position x 2 =. (b) If a charged particle (q = 4nC, m = 1.5ng) is released from rest at x 1, what are its kinetic energy K 2 and its velocity v 2 when it reaches position x 2? Q = 5nC Solution: x = 0 x 1= 3m x 2= (a) V 1 = k Q x 1 = 15V, V 2 = k Q x 2 = 7.5V. (b) U = q(v 2 V 1 ) = (4nC)( 7.5V) = 30nJ K = U = 30nJ. K = K 2 = 1 r 2K2 2 mv2 2 v 2 = m = 200m/s. 2/9/2015 [tsl332 19/21]

23 Unit Exam I: Problem #1 (Fall 10) Consider two point charges positioned as shown. +7nC (a) Find the magnitude of the electric field at point A. (b) Find the electric potential at point A. (c) Find the magnitude of the electric field at point B. (d) Find the electric potential at point B. 5m A 5m B 8m 7nC 2/9/2015 [tsl398 20/21]

24 Unit Exam I: Problem #1 (Fall 10) Consider two point charges positioned as shown. +7nC (a) Find the magnitude of the electric field at point A. (b) Find the electric potential at point A. (c) Find the magnitude of the electric field at point B. (d) Find the electric potential at point B. 5m A 5m Solution: (a) E A = 2k 7nC = 2(2.52V/m) = 5.04V/m. (5m) 2 B 8m 7nC 2/9/2015 [tsl398 20/21]

25 Unit Exam I: Problem #1 (Fall 10) Consider two point charges positioned as shown. +7nC (a) Find the magnitude of the electric field at point A. (b) Find the electric potential at point A. (c) Find the magnitude of the electric field at point B. (d) Find the electric potential at point B. 5m A 5m Solution: (a) E A = 2k 7nC = 2(2.52V/m) = 5.04V/m. (5m) 2 B 8m 7nC (b) V A = k (+7nC) 5m + k ( 7nC) 5m = 12.6V 12.6V = 0. 2/9/2015 [tsl398 20/21]

26 Unit Exam I: Problem #1 (Fall 10) Consider two point charges positioned as shown. (a) Find the magnitude of the electric field at point A. (b) Find the electric potential at point A. (c) Find the magnitude of the electric field at point B. (d) Find the electric potential at point B. Solution: (a) E A = 2k 7nC = 2(2.52V/m) = 5.04V/m. (5m) 2 (b) V A = k (+7nC) 5m + k ( 7nC) 5m s (c) E B = k 7nC () 2 «2 + k 7nC (8m) 2 = 12.6V 12.6V = 0. +7nC B 5m A 8m 5m 7nC «2 E B = q (1.75V/m) 2 + (0.98V/m) 2 = 2.01V/m. 2/9/2015 [tsl398 20/21]

27 Unit Exam I: Problem #1 (Fall 10) Consider two point charges positioned as shown. (a) Find the magnitude of the electric field at point A. (b) Find the electric potential at point A. (c) Find the magnitude of the electric field at point B. (d) Find the electric potential at point B. Solution: (a) E A = 2k 7nC = 2(2.52V/m) = 5.04V/m. (5m) 2 (b) V A = k (+7nC) 5m + k ( 7nC) 5m s (c) E B = k 7nC () 2 (d) V B = k (+7nC) «2 + k 7nC (8m) 2 + k( 7nC) 8m = 12.6V 12.6V = 0. +7nC B 5m A 8m 5m 7nC «2 E B = q (1.75V/m) 2 + (0.98V/m) 2 = 2.01V/m. = 10.5V 7.9V = 2.6V. 2/9/2015 [tsl398 20/21]

28 Unit Exam I: Problem #1 (Spring 14) Consider two point charges positioned as shown. Find the magnitude of the electric field at point A. Find the electric potential at point B. Find the magnitude of the electric field at point C. Find the electric potential at point D. +5nC 3m A 8m 3m C 4m D B 8m 9nC 2/9/2015 [tsl469 21/21]

29 Unit Exam I: Problem #1 (Spring 14) Consider two point charges positioned as shown. Find the magnitude of the electric field at point A. Find the electric potential at point B. Find the magnitude of the electric field at point C. Find the electric potential at point D. +5nC 3m A 8m 3m C 4m D Solution: B 8m 9nC E A = k 5nC (3m) 2 + k 9nC (7m) 2 = 5.00V/m V/m = 6.65V/m. 2/9/2015 [tsl469 21/21]

30 Unit Exam I: Problem #1 (Spring 14) Consider two point charges positioned as shown. Find the magnitude of the electric field at point A. Find the electric potential at point B. Find the magnitude of the electric field at point C. Find the electric potential at point D. +5nC 3m A 8m 3m C 4m D Solution: B 8m 9nC E A = k 5nC (3m) 2 + k 9nC (7m) 2 V B = k (+5nC) + k( 9nC) 8m = 5.00V/m V/m = 6.65V/m. = 7.50V 10.13V = 2.63V. 2/9/2015 [tsl469 21/21]

31 Unit Exam I: Problem #1 (Spring 14) Consider two point charges positioned as shown. Find the magnitude of the electric field at point A. Find the electric potential at point B. Find the magnitude of the electric field at point C. Find the electric potential at point D. +5nC 3m A 8m 3m C 4m D B 8m 9nC Solution: E A = k 5nC (3m) 2 + k 9nC (7m) 2 = 5.00V/m V/m = 6.65V/m. V B = k (+5nC) + k( 9nC) 8m E C = k 5nC () 2 + k 9nC (4m) 2 = 7.50V 10.13V = 2.63V. = 1.25V/m V/m = 6.31V/m. 2/9/2015 [tsl469 21/21]

32 Unit Exam I: Problem #1 (Spring 14) Consider two point charges positioned as shown. Find the magnitude of the electric field at point A. Find the electric potential at point B. Find the magnitude of the electric field at point C. Find the electric potential at point D. +5nC 3m A 8m 3m C 4m D B 8m 9nC Solution: E A = k 5nC (3m) 2 + k 9nC (7m) 2 = 5.00V/m V/m = 6.65V/m. V B = k (+5nC) + k( 9nC) 8m E C = k 5nC () 2 + k 9nC (4m) 2 = 7.50V 10.13V = 2.63V. = 1.25V/m V/m = 6.31V/m. V D = k (+5nC) 8m + k ( 9nC) = 5.63V 13.5V = 7.87V. 2/9/2015 [tsl469 21/21]

Work and Energy. v f. v i. F(x ) F(x ) x f. Consider a block of mass m moving along the x-axis. Conservative force acting on block: F = F(x) Z xf

Work and Energy. v f. v i. F(x ) F(x ) x f. Consider a block of mass m moving along the x-axis. Conservative force acting on block: F = F(x) Z xf Work and Energy Consider a block of mass m moving along the x-axis. Conservative force acting on block: F = F(x) Work done by F(x) on block: W if = Kinetic energy of block: K = 1 2 mv2 Potential energy

More information

02. Electric Field II

02. Electric Field II Universit of Rhode Island DigitalCommons@URI PHY 24: Elementar Phsics II Phsics Course Materials 215 2. Electric Field II Gerhard Müller Universit of Rhode Island, gmuller@uri.edu Creative Commons License

More information

01. Introduction and Electric Field I

01. Introduction and Electric Field I University of Rhode Island DigitalCommons@URI PHY 204: lementary Physics II Physics Course Materials 2015 01. Introduction and lectric Field I Gerhard Müller University of Rhode Island, gmuller@uri.edu

More information

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License.

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License. University of Rhode Island DigitalCommons@URI PHY 204: Elementary Physics II Physics Course Materials 2015 08. Capacitors II Gerhard Müller University of Rhode Island, gmuller@uri.edu Creative Commons

More information

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License.

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License. University of Rhode Island DigitalCommons@URI PHY 204: Elementary Physics II Physics Course Materials 2015 07. Capacitors I Gerhard Müller University of Rhode Island, gmuller@uri.edu Creative Commons License

More information

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License.

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License. University of Rhode Island DigitalCommons@URI PHY 204: Elementary Physics II Physics Course Materials 2015 12. Magnetic Field I Gerhard Müller University of Rhode Island, gmuller@uri.edu Creative Commons

More information

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License.

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License. University of Rhode Island DigitalCommons@URI PHY 204: Elementary Physics II Physics Course Materials 2015 18. RL Circuits Gerhard Müller University of Rhode Island, gmuller@uri.edu Creative Commons License

More information

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License.

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License. University of Rhode Island DigitalCommons@URI PHY 204: Elementary Physics II Physics Course Materials 2015 09. Resistors I Gerhard Müller University of Rhode Island, gmuller@uri.edu Creative Commons License

More information

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License.

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License. University of Rhode Island DigitalCommons@URI PHY 204: Elementary Physics II Physics Course Materials 2015 10. Resistors II Gerhard Müller University of Rhode Island, gmuller@uri.edu Creative Commons License

More information

14. Magnetic Field III

14. Magnetic Field III University of Rhode sland DigitalCommons@UR PHY 204: Elementary Physics Physics Course Materials 2015 14. Magnetic Field Gerhard Müller University of Rhode sland, gmuller@uri.edu Creative Commons License

More information

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License.

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License. University of Rhode Island DigitalCommons@URI PHY 204: Elementary Physics II Physics Course Materials 2015 16. Faraday's Law Gerhard Müller University of Rhode Island, gmuller@uri.edu Creative Commons

More information

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License.

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License. University of Rhode Island DigitalCommons@URI PHY 204: Elementary Physics II Physics Course Materials 2015 11. RC Circuits Gerhard Müller University of Rhode Island, gmuller@uri.edu Creative Commons License

More information

13. Magnetic Field II

13. Magnetic Field II University of Rhode sland DigitalCommons@UR PHY 204: Elementary Physics Physics Course Materials 2015 13. Magnetic Field Gerhard Müller University of Rhode sland, gmuller@uri.edu Creative Commons License

More information

03. Electric Field III and Electric Flux

03. Electric Field III and Electric Flux Universit of Rhode Island DigitalCommons@URI PHY 204: lementar Phsics II Phsics Course Materials 2015 03. lectric Field III and lectric Flu Gerhard Müller Universit of Rhode Island, gmuller@uri.edu Creative

More information

02. Newtonian Gravitation

02. Newtonian Gravitation University of Rhode Island DigitalCommons@URI Classical Dynamics Physics Course Materials 2015 02. Newtonian Gravitation Gerhard Müller University of Rhode Island, gmuller@uri.edu Creative Commons License

More information

Chapter 17. Electric Potential Energy and the Electric Potential

Chapter 17. Electric Potential Energy and the Electric Potential Chapter 17 Electric Potential Energy and the Electric Potential Consider gravity near the surface of the Earth The gravitational field is uniform. This means it always points in the same direction with

More information

19. LC and RLC Oscillators

19. LC and RLC Oscillators University of Rhode Island Digitaloons@URI PHY 204: Eleentary Physics II Physics ourse Materials 2015 19. L and RL Oscillators Gerhard Müller University of Rhode Island, guller@uri.edu reative oons License

More information

14. Ideal Quantum Gases II: Fermions

14. Ideal Quantum Gases II: Fermions University of Rhode Island DigitalCommons@URI Equilibrium Statistical Physics Physics Course Materials 25 4. Ideal Quantum Gases II: Fermions Gerhard Müller University of Rhode Island, gmuller@uri.edu

More information

20. Alternating Currents

20. Alternating Currents University of hode sland DigitalCommons@U PHY 204: Elementary Physics Physics Course Materials 2015 20. lternating Currents Gerhard Müller University of hode sland, gmuller@uri.edu Creative Commons License

More information

03. Simple Dynamical Systems

03. Simple Dynamical Systems University of Rhode Island DigitalCommons@URI Classical Dynamics Physics Course Materials 2015 03. Simple Dynamical Systems Gerhard Müller University of Rhode Island, gmuller@uri.edu Creative Commons License

More information

Chatper 7 - Kinetic Energy and Work

Chatper 7 - Kinetic Energy and Work Chatper 7 - and Energy and Examples The release of atomic energy has not created a new problem. It has merely made more urgent the necessity of solving an existing one. - Albert Einstein David J. Starling

More information

Slide 1 / Which of the following represents the electric field map due to a single positive charge? A B C

Slide 1 / Which of the following represents the electric field map due to a single positive charge? A B C Slide 1 / 21 1 Which of the following represents the electric field map due to a single positive charge? Slide 2 / 21 2 Which of the following represents the electric field map due to a single negative

More information

Physics 12 ELECTROSTATICS

Physics 12 ELECTROSTATICS Physics 12 ELECTROSTATICS F = kq 1Q 2 r2 E = V d V = kq r E p = kq 1Q 2 r F = qe V = E p Q 1 000 000 Volts 1 000 000 Volts NAME: Block: Text References 3 rd Ed. Giancolli Pg. 416-30 4 th Ed. Giancolli

More information

Particle in Uniform Electric or Gravitational Field

Particle in Uniform Electric or Gravitational Field Particle in Uniform Electric or Gravitational Field particle charge mass electron q e = e m e = 9.19 1 31 kg proton q p = +e m p = 1.673 1 27 kg neutron q n = m n = 1.675 1 27 kg Elementar charge: e =

More information

Electric Fields Part 1: Coulomb s Law

Electric Fields Part 1: Coulomb s Law Electric Fields Part 1: Coulomb s Law F F Last modified: 07/02/2018 Contents Links Electric Charge & Coulomb s Law Electric Charge Coulomb s Law Example 1: Coulomb s Law Electric Field Electric Field Vector

More information

15. Hamiltonian Mechanics

15. Hamiltonian Mechanics University of Rhode Island DigitalCommons@URI Classical Dynamics Physics Course Materials 2015 15. Hamiltonian Mechanics Gerhard Müller University of Rhode Island, gmuller@uri.edu Creative Commons License

More information

Chapter 8: Potential Energy and Conservation of Energy Work and kinetic energy are energies of motion.

Chapter 8: Potential Energy and Conservation of Energy Work and kinetic energy are energies of motion. Chapter 8: Potential Energy and Conservation of Energy Work and kinetic energy are energies of motion. K = K f K i = 1 2 mv 2 f rf = v v F dr Consider a vertical spring oscillating with mass m attached

More information

2. E A 3. E A 4. E A 5. E A

2. E A 3. E A 4. E A 5. E A west (mrw3223) HW 23 lyle (16001) 1 This print-out should have 32 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. Reading assignment: Hecht

More information

13. Rigid Body Dynamics II

13. Rigid Body Dynamics II University of Rhode Island DigitalCommons@URI Classical Dynamics Physics Course Materials 2015 13. Rigid Body Dynamics II Gerhard Müller University of Rhode Island, gmuller@uri.edu Creative Commons License

More information

Electric Potential. Capacitors (Chapters 28, 29)

Electric Potential. Capacitors (Chapters 28, 29) Electric Potential. Capacitors (Chapters 28, 29) Electric potential energy, U Electric potential energy in a constant field Conservation of energy Electric potential, V Relation to the electric field strength

More information

14.4 Change in Potential Energy and Zero Point for Potential Energy

14.4 Change in Potential Energy and Zero Point for Potential Energy 14.4 Change in Potential Energy and Zero Point for Potential Energy We already calculated the work done by different conservative forces: constant gravity near the surface of the earth, the spring force,

More information

12. Rigid Body Dynamics I

12. Rigid Body Dynamics I University of Rhode Island DigitalCommons@URI Classical Dynamics Physics Course Materials 015 1. Rigid Body Dynamics I Gerhard Müller University of Rhode Island, gmuller@uri.edu Creative Commons License

More information

Conservation of Energy

Conservation of Energy Lecture 3 Chapter 8 Physics I 03.0.04 Conservation of Energy Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi Lecture Capture: http://echo360.uml.edu/danylov03/physicsspring.html

More information

06. Lagrangian Mechanics II

06. Lagrangian Mechanics II University of Rhode Island DigitalCommons@URI Classical Dynamics Physics Course Materials 2015 06. Lagrangian Mechanics II Gerhard Müller University of Rhode Island, gmuller@uri.edu Creative Commons License

More information

PHYS ST semester Dr. Nadyah Alanazi. Lecture 11

PHYS ST semester Dr. Nadyah Alanazi. Lecture 11 1 PHYS 104 1 ST semester 1439-1440 Dr. Nadyah Alanazi Lecture 11 25.1 Potential Difference and Electric Potential When a test charge q 0 is placed in an electric field E created by some source charge,

More information

CHAPTER 19 - ELECTRIC POTENTIAL ENERGY AND ELECTRIC POTENTIAL. Sections 1-5

CHAPTER 19 - ELECTRIC POTENTIAL ENERGY AND ELECTRIC POTENTIAL. Sections 1-5 CHAPTER 19 - ELECTRIC POTENTIAL ENERGY AND ELECTRIC POTENTIAL Sections 1-5 Objectives: After completing this unit, you should be able to: Understand an apply the concepts of electric potential energy,

More information

PHYS102 Previous Exam Problems. Electric Potential

PHYS102 Previous Exam Problems. Electric Potential PHYS102 Previous Exam Problems CHAPTER 24 Electric Potential Electric potential energy of a point charge Calculating electric potential from electric field Electric potential of point charges Calculating

More information

Book page. Coulombs Law

Book page. Coulombs Law Book page Coulombs Law A Coulomb torsion balance A Coulomb torsion balance is used to measure the force between two charged objects Coulomb's Torsion Balance Two conducting spheres fixed on insulating

More information

Dr. Gundersen Phy 205DJ Test 2 22 March 2010

Dr. Gundersen Phy 205DJ Test 2 22 March 2010 Signature: Idnumber: Name: Do only four out of the five problems. The first problem consists of five multiple choice questions. If you do more only your FIRST four answered problems will be graded. Clearly

More information

Electric Potential (Chapter 25)

Electric Potential (Chapter 25) Electric Potential (Chapter 25) Electric potential energy, U Electric potential energy in a constant field Conservation of energy Electric potential, V Relation to the electric field strength The potential

More information

Electric Charge and Electric Field AP Physics 4 Lecture Notes

Electric Charge and Electric Field AP Physics 4 Lecture Notes Electric Charge and Electric Field AP Physics 4 Lecture Notes Coulomb s Law The Electric Field Field Lines Electric Fields and Conductors Coulomb s law: Coulomb s Law Force (N) F F F k r F F F r Charge

More information

10. Scattering from Central Force Potential

10. Scattering from Central Force Potential University of Rhode Island DigitalCommons@URI Classical Dynamics Physics Course Materials 215 1. Scattering from Central Force Potential Gerhard Müller University of Rhode Island, gmuller@uri.edu Creative

More information

Semester 2 Physics (SF 026) Lecture: BP 3 by Yew Sze Fiona Website:

Semester 2 Physics (SF 026) Lecture: BP 3 by Yew Sze Fiona Website: Semester 2 Physics (SF 026) Lecture: BP 3 by Yew Sze Ling @ Fiona Website: http://yslphysics.weebly.com/ Chapter 1: Electrostatics The study of electric charges at rest, the forces between them and the

More information

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License.

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License. University of Rhode Island DigitalCommons@URI Equilibrium Statistical Physics Physics Course Materials 2015 07. Kinetic Theory I Gerhard Müller University of Rhode Island, gmuller@uri.edu Creative Commons

More information

Physics 1202: Lecture 3 Today s Agenda

Physics 1202: Lecture 3 Today s Agenda Physics 1202: Lecture 3 Today s Agenda Announcements: Lectures posted on: www.phys.uconn.edu/~rcote/ HW assignments, solutions etc. Homework #1: On Masterphysics: due this coming Friday Go to the syllabus

More information

Work and kinetic energy. If a net force is applied on an object, the object may

Work and kinetic energy. If a net force is applied on an object, the object may Work and kinetic energy If a net force is applied on an object, the object may CHAPTER 6 WORK AND ENERGY experience a change in position, i.e., a displacement. When a net force is applied over a distance,

More information

4 Chapter. Electric Potential

4 Chapter. Electric Potential 4 Chapter Electric Potential 4.1 Potential and Potential Energy... 4-3 4.2 Electric Potential in a Uniform Field... 4-7 4.3 Electric Potential due to Point Charges... 4-8 4.3.1 Potential Energy in a System

More information

Electric Potential Practice Problems

Electric Potential Practice Problems Electric Potential Practice Problems AP Physics Name Multiple Choice 1. A negative charge is placed on a conducting sphere. Which statement is true about the charge distribution (A) Concentrated at the

More information

If you have a conflict, you should have already requested and received permission from Prof. Shapiro to take the make-up exam.

If you have a conflict, you should have already requested and received permission from Prof. Shapiro to take the make-up exam. Reminder: Exam this Sunday Nov. 9. Chapters 5. 5.4, 3.4,.0, 6, 7. Time: 6:0 7:30 PM Look up locations online. Bring calculator and formula sheet. If you have a conflict, you should have already requested

More information

Coulomb s Law. Phys102 Lecture 2. Key Points. Coulomb s Law The electric field (E is a vector!) References

Coulomb s Law. Phys102 Lecture 2. Key Points. Coulomb s Law The electric field (E is a vector!) References Phys102 Lecture 2 Phys102 Lecture 2-1 Coulomb s Law Key Points Coulomb s Law The electric field (E is a vector!) References SFU Ed: 21-5,6,7,8,9,10. 6 th Ed: 16-6,7,8,9,+. Phys102 Lecture 2 Phys102 Lecture

More information

PHYS102 Previous Exam Problems. Electric Fields

PHYS102 Previous Exam Problems. Electric Fields PHYS102 Previous Exam Problems CHAPTER 22 Electric Fields Electric field Point charge in an electric field Electric dipole 1. Two identical charges, each of charge Q, are positioned at points A (5.0 m,

More information

Lecture 17. PHYC 161 Fall 2016

Lecture 17. PHYC 161 Fall 2016 Lecture 17 PHYC 161 Fall 2016 Electric potential Potential is potential energy per unit charge. The potential of a with respect to b (V ab = V a V b ) equals the work done by the electric force when a

More information

Objects can be charged by rubbing

Objects can be charged by rubbing Electrostatics Objects can be charged by rubbing Charge comes in two types, positive and negative; like charges repel and opposite charges attract Electric charge is conserved the arithmetic sum of the

More information

Electrostatics. 3) positive object: lack of electrons negative object: excess of electrons. Particle Mass Electric Charge. m e = 9.

Electrostatics. 3) positive object: lack of electrons negative object: excess of electrons. Particle Mass Electric Charge. m e = 9. Electrostatics 1) electric charge: 2 types of electric charge: positive and negative 2) charging by friction: transfer of electrons from one object to another 3) positive object: lack of electrons negative

More information

Chapter 7 Potential Energy and Energy Conservation

Chapter 7 Potential Energy and Energy Conservation Chapter 7 Potential Energy and Energy Conservation We saw in the previous chapter the relationship between work and kinetic energy. We also saw that the relationship was the same whether the net external

More information

Chapters 10 & 11: Energy

Chapters 10 & 11: Energy Chapters 10 & 11: Energy Power: Sources of Energy Tidal Power SF Bay Tidal Power Project Main Ideas (Encyclopedia of Physics) Energy is an abstract quantity that an object is said to possess. It is not

More information

PHYSICS 12 NAME: Electrostatics Review

PHYSICS 12 NAME: Electrostatics Review NAME: Electrostatics Review 1. The diagram below shows two positive charges of magnitude Q and 2Q. Which vector best represents the direction of the electric field at point P, which is equidistant from

More information

Module 12: Work and the Scalar Product

Module 12: Work and the Scalar Product Module 1: Work and the Scalar Product 1.1 Scalar Product (Dot Product) We shall introduce a vector operation, called the dot product or scalar product that takes any two vectors and generates a scalar

More information

13. Ideal Quantum Gases I: Bosons

13. Ideal Quantum Gases I: Bosons University of Rhode Island DigitalCommons@URI Equilibrium Statistical Physics Physics Course Materials 5 3. Ideal Quantum Gases I: Bosons Gerhard Müller University of Rhode Island, gmuller@uri.edu Creative

More information

PHYSICS 12 NAME: Electrostatics Review

PHYSICS 12 NAME: Electrostatics Review NAME: Electrostatics Review 1. The diagram below shows two positive charges of magnitude Q and 2Q. Which vector best represents the direction of the electric field at point P, which is equidistant from

More information

MTE1 results. Mean 75% = 90/120

MTE1 results. Mean 75% = 90/120 MTE1 results Mean 75% = 90/120 Scores available at Learn@UW, your TAs have exams If your score is an F or a D, talk to us and your TAs for suggestions on how to improve From last times Electric charges

More information

In-Class Problems 20-21: Work and Kinetic Energy Solutions

In-Class Problems 20-21: Work and Kinetic Energy Solutions MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01T Fall Term 2004 In-Class Problems 20-21: Work and Kinetic Energy Solutions In-Class-Problem 20 Calculating Work Integrals a) Work

More information

Chapter 23 Electric Potential (Voltage)

Chapter 23 Electric Potential (Voltage) Chapter 23 Electric Potential (Voltage) Electric potential energy Recall how a conservative force is related to the potential energy associated with that force: The electric potential energy: Change in

More information

Introduction to Charges. BCLN PHYSICS 12 - Rev. Sept/2012

Introduction to Charges. BCLN PHYSICS 12 - Rev. Sept/2012 Electrostatics ~ Learning Guide Name: Instructions: Using a pencil, answer the following questions. The Pre-Reading is marked, based on effort, completeness, and neatness (not accuracy). The rest of the

More information

Chapter 25. Electric Potential

Chapter 25. Electric Potential Chapter 25 Electric Potential Outline 25.1 Potential difference and electric Potential 25.2 Potential Difference and electric field 25.3 Electric Potential and Potential energy due to point charges 25.1

More information

Electrostatics Notes 1 Charges and Coulomb s Law

Electrostatics Notes 1 Charges and Coulomb s Law Electrostatics Notes 1 Charges and Coulomb s Law Matter is made of particles which are or charged. The unit of charge is the ( ) Charges are, meaning that they cannot be It is thought that the total charge

More information

04. Random Variables: Concepts

04. Random Variables: Concepts University of Rhode Island DigitalCommons@URI Nonequilibrium Statistical Physics Physics Course Materials 215 4. Random Variables: Concepts Gerhard Müller University of Rhode Island, gmuller@uri.edu Creative

More information

Electric Potential of Charged Rod

Electric Potential of Charged Rod Electric Potential of Charged Rod Charge per unit length: λ = Q/L y dq = λ d Charge on slice d: dq = λd dv d L Electric potential generated by slice d: dv = kdq = kλd Electric potential generated by charged

More information

Phys 102 Lecture 4 Electric potential energy & work

Phys 102 Lecture 4 Electric potential energy & work Phys 102 Lecture 4 Electric potential energy & work 1 Today we will... Learn about the electric potential energy Relate it to work Ex: charge in uniform electric field, point charges Apply these concepts

More information

Chapter 21 Electric Potential

Chapter 21 Electric Potential Chapter 21 Electric Potential Chapter Goal: To calculate and use the electric potential and electric potential energy. Slide 21-1 Chapter 21 Preview Looking Ahead Text: p. 665 Slide 21-2 Review of Potential

More information

Kinematics (special case) Dynamics gravity, tension, elastic, normal, friction. Energy: kinetic, potential gravity, spring + work (friction)

Kinematics (special case) Dynamics gravity, tension, elastic, normal, friction. Energy: kinetic, potential gravity, spring + work (friction) Kinematics (special case) a = constant 1D motion 2D projectile Uniform circular Dynamics gravity, tension, elastic, normal, friction Motion with a = constant Newton s Laws F = m a F 12 = F 21 Time & Position

More information

PHY2054 Summer 2006 Exam 1 06 June 2006

PHY2054 Summer 2006 Exam 1 06 June 2006 PHY2054 Summer 2006 Exam 1 06 June 2006 Solutions Unless otherwise indicated, (1) is the correct answer. Solutions are, of necessity (due to the writer's self-taught & primitive word-processing skills),

More information

P = dw dt. P = F net. = W Δt. Conservative Force: P ave. Net work done by a conservative force on an object moving around every closed path is zero

P = dw dt. P = F net. = W Δt. Conservative Force: P ave. Net work done by a conservative force on an object moving around every closed path is zero Power Forces Conservative Force: P ave = W Δt P = dw dt P = F net v Net work done by a conservative force on an object moving around every closed path is zero Non-conservative Force: Net work done by a

More information

AP* Electrostatics Free Response Questions

AP* Electrostatics Free Response Questions AP* Electrostatics Free Response Questions 1987 Q2 Object I, shown above, has a charge of +3 10 6 coulomb and a mass of 0.0025 kilogram. (a) What is the electric potential at point P, 0.30 meter from object

More information

What You Already Know

What You Already Know What You Already Know Coulomb s law Electric fields Gauss law Electric fields for several configurations Point Line Plane (nonconducting) Sheet (conducting) Ring (along axis) Disk (along axis) Sphere Cylinder

More information

Electric Potential Energy

Electric Potential Energy Electric Potential Energy the electric potential energy of two charges depends on the distance between the charges when two like charges are an infinite distance apart, the potential energy is zero An

More information

Chapter 8. Potential Energy and Energy Conservation

Chapter 8. Potential Energy and Energy Conservation Chapter 8 Potential Energy and Energy Conservation P. Lam 7_18_2018 Learning Goals for Chapter 8 Learn the following concepts: conservative forces, potential energy, and conservation of mechanical energy.

More information

Physics 2049 Exam 1 Spring 2002

Physics 2049 Exam 1 Spring 2002 Physics 49 Exam 1 Spring q r1 q1 r13 q3 1. In the figure q 1 = 3µC, q = 4µC, q 3 = 5µC, r 1 = 9m, r 13 = 1m. Compute the magnitude of the total force on q 3. F 3NET = F 31 + F 3 = kq 3q 1 î + kq ( 3q )

More information

Rutgers University Department of Physics & Astronomy. 01:750:271 Honors Physics I Fall Lecture 10. Home Page. Title Page. Page 1 of 37.

Rutgers University Department of Physics & Astronomy. 01:750:271 Honors Physics I Fall Lecture 10. Home Page. Title Page. Page 1 of 37. Rutgers University Department of Physics & Astronomy 01:750:271 Honors Physics I Fall 2015 Lecture 10 Page 1 of 37 Midterm I summary 100 90 80 70 60 50 40 30 20 39 43 56 28 11 5 3 0 1 Average: 82.00 Page

More information

Potentials and Fields

Potentials and Fields Potentials and Fields Review: Definition of Potential Potential is defined as potential energy per unit charge. Since change in potential energy is work done, this means V E x dx and E x dv dx etc. The

More information

IB-1 Physics Electrostatics Practice Questions. e +4e A. B. C. D.

IB-1 Physics Electrostatics Practice Questions. e +4e A. B. C. D. 1. A plastic rod is rubbed with a cloth. At the end of the process, the rod is found to be positively charged and the cloth is found to be uncharged. This involves the movement of A. positive charge from

More information

Motion of Charged Particles in Electric Fields. Part A Motion of a charged particle due to the presence of another charged particle

Motion of Charged Particles in Electric Fields. Part A Motion of a charged particle due to the presence of another charged particle Motion of Charged Particles in Electric Fields We will be looking at two situations in which a charged particle is moving in an electric field. The first situation occurs when the motion of the charged

More information

Electrostatics Notes 2 Electric Field on a Single Charge

Electrostatics Notes 2 Electric Field on a Single Charge Electrostatics Notes 2 Electric Field on a Single Charge There are many similarities between gravitational and electrostatic forces. One such similarity is that both forces can be exerted on objects that

More information

Study Guide #1. L. Colonna-Romano/T. Keil. Electricity and Magnetism

Study Guide #1. L. Colonna-Romano/T. Keil. Electricity and Magnetism PH1120 Electricity and Magnetism L. Colonna-Romano/T. Keil Term B98 Study Guide #1 This is the first in a series of four Study Guides that have been designed to help you get the most out of this course.

More information

Chapter 20. Electric Potential Electric Potential Energy

Chapter 20. Electric Potential Electric Potential Energy Chapter 20 Electric Potential Electric Potential Energy CONSERVTIVE FORCES conservative force gives back work that has been done against it Gravitational and electrostatic forces are conservative Friction

More information

Física Básica Experimental I Cuestiones Tema VII. Electrostática. Soluciones incluidas. 1.

Física Básica Experimental I Cuestiones Tema VII. Electrostática. Soluciones incluidas. 1. 1. A cubical surface with no charge enclosed and with sides 2.0 m long is oriented with right and left faces perpendicular to a uniform electric field E of (1.6 10 5 N/C) î. The net electric flux E through

More information

Chapter 25. Electric Potential

Chapter 25. Electric Potential Chapter 25 Electric Potential Electric Potential Electromagnetism has been connected to the study of forces in previous chapters. In this chapter, electromagnetism will be linked to energy. By using an

More information

Power. Power is the time rate at which work W is done by a force Average power. (energy per time) P = dw/dt = (Fcosφ dx)/dt = F v cosφ= F.

Power. Power is the time rate at which work W is done by a force Average power. (energy per time) P = dw/dt = (Fcosφ dx)/dt = F v cosφ= F. Power Power is the time rate at which work W is done by a force Aerage power P ag = W/ t Instantaneous power (energy per time) P = dw/dt = (Fcosφ dx)/dt = F cosφ= F. Unit: watt 1 watt = 1 W = 1 J/s 1 horsepower

More information

charge of opposite signs attract / charges of the same sign repel

charge of opposite signs attract / charges of the same sign repel VISUAL PHYSICS ONLINE MODULE 4.1 ELECTRICITY ELECTRIC FIELD ELECTRIC POTENTIAL QUESTIONS and PROBLEMS (with ANSWRES) ex41b ex41c electric force F E [N] charge of opposite signs attract / charges of the

More information

Chapter 14 Potential Energy and Conservation of Energy

Chapter 14 Potential Energy and Conservation of Energy Chapter 4 Potential Energy and Conservation of Energy Chapter 4 Potential Energy and Conservation of Energy... 2 4. Conservation of Energy... 2 4.2 Conservative and Non-Conservative Forces... 3 4.3 Changes

More information

Chapter 22 Electric Potential (Voltage)

Chapter 22 Electric Potential (Voltage) Chapter 22 Electric Potential (Voltage) Question 29.5 Work and Electric Potential I Which requires the most work, to move a positive charge from P to points 1, 2, 3 or 4? All points are the same distance

More information

Lecture 6.1 Work and Energy During previous lectures we have considered many examples, which can be solved using Newtonian approach, in particular,

Lecture 6.1 Work and Energy During previous lectures we have considered many examples, which can be solved using Newtonian approach, in particular, Lecture 6. Work and Energy During previous lectures we have considered many examples, which can be solved using Newtonian approach, in particular, Newton's second law. However, this is not always the most

More information

Electric Potential. David J. Starling Penn State Hazleton PHYS 212. Electricity is really just organized lightning. - George Carlin.

Electric Potential. David J. Starling Penn State Hazleton PHYS 212. Electricity is really just organized lightning. - George Carlin. Electricity is really just organized lightning. - George Carlin David J. Starling Penn State Hazleton PHYS 212 Since the electric force is so similar to gravity, might it be conservative? Yes! If we move

More information

Handout 3: Electric potential and electric potential energy. Electric potential

Handout 3: Electric potential and electric potential energy. Electric potential Handout 3: Electric potential and electric potential energy Electric potential Consider a charge + fixed in space as in Figure. Electric potential V at any point in space is defined as the work done by

More information

Chapter 19 Electric Potential and Electric Field Sunday, January 31, Key concepts:

Chapter 19 Electric Potential and Electric Field Sunday, January 31, Key concepts: Chapter 19 Electric Potential and Electric Field Sunday, January 31, 2010 10:37 PM Key concepts: electric potential electric potential energy the electron-volt (ev), a convenient unit of energy when dealing

More information

Chapter 6 Work and Energy

Chapter 6 Work and Energy Chapter 6 Work and Energy Midterm exams will be available next Thursday. Assignment 6 Textbook (Giancoli, 6 th edition), Chapter 6: Due on Thursday, November 5 1. On page 162 of Giancoli, problem 4. 2.

More information

http://xkcd.com/567/ electrical energy & capacitance today & tomorrow first: wrap up Gauss law, then potential capacitors/dielectrics tomorrow rest of the week: circuits/current/resistance NEXT MON: exam

More information

Exam 1--PHYS 102--S17

Exam 1--PHYS 102--S17 Name: Exam 1--PHYS 102--S17 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The up-quark, u, has an elementary charge of +(2/3)e and the down-quark, d,

More information

CHAPTER 22. The Electric Field I: Discrete Charge Distributions

CHAPTER 22. The Electric Field I: Discrete Charge Distributions CHAPTER 1* If the sign convention for charge were changed so that the charge on the electron were positive and the charge on the proton were negative, would Coulomb's law still be written the same? Yes

More information

Physics 1302, Exam 1 Review

Physics 1302, Exam 1 Review c V Andersen, 2006 1 Physics 1302, Exam 1 Review The following is a list of things you should definitely know for the exam, however, the list is not exhaustive. You are responsible for all the material

More information