PHYS 221 General Physics II

Transcription

1 PHYS 221 General Physics II Elec. Potential Energy, Voltage, Equipotentials Spring 2015 Assigned Reading: Lecture 4

2 Review: Gauss Law Last Lecture E q enc o E EAcos Gauss Law Very useful to determine E when there is symmetry Phys 221 Spring 2014 Lecture 04 2

3 From Mechanics (PHYS 220) Energy Kinetic Energy: associated with the state of motion KE 1 2 mv2 Potential Energy: associated with the configuration of the system PE W Conservative Forces: W Fx cos W=F x if F and x are parallel Work done by a conservative force is independent of path. PE(gravity) mgh PE(spring) k 2 x2 Phys 221 Spring 2014 Lecture 04 3

4 Potential Energy of Two Point Charges m1m G r U g 2 PE elec k q 1 q 2 r Gravity: always attraction. U is more negative ( lower ) when objects are closer q 1 q 2 < 0 : attraction. U is more negative ( lower ) when objects are closer q 1 q 2 > 0 : repulsion. U is lower when objects are farther apart Phys 221 Spring 2014 Lecture 04 4

5 Potential Energy: Gravitational vs Electric Gravitational potential energy Electric potential energy PE = -W grav.field W = F. d. cos() m1m 2 F g G 2 r PE=0 at r= PE G m m 1 2 r PE = -W elec.field W = F. d. cos() q1q 2 F e k 2 r PE k q q 1 2 r Phys 221 Spring 2014 Lecture 04 5

6 BB i>clicker question BB C F A B What is the direction of the force on the negative charge at point A? 1) left 2) right 3) up Uniform E Phys 221 Spring 2014 Lecture 04 6

7 BB i>clicker question BB C A B When a negative charge is moved from A to C the ELECTRIC force does 1) positive work. 2) zero work. 3) negative work. Uniform E Phys 221 Spring 2014 Lecture 04 7

8 Zero because the path is perpendicular to the field W Fx cos qex cos 0 F F F F F motion C A Uniform E B When a negative charge is moved from A to C the ELECTRIC force does A. positive work. B. zero work. C. negative work. Phys 221 Spring 2014 Lecture 04 8

9 Potential Energy of Several Point Charges: An Example with 3 charges PE 13 k q 1q 3 q 1 -q 3 PE 12 k q 1 q 2 r 12 PE 23 k q 2q 3 q 2 r 13 r 23 Total potential energy PE: PE PE 12 PE 23 PE 13 PE k q 1q 2 q 2q 3 q 1q 3 r 12 r 23 r 13 Potential energy of many charges is a scalar sum of potential energies of all the pairs of charges in the system. Note: each pair should be counted only once. Phys 221 Spring 2014 Lecture 04 9

10 Electric Potential q 5 q 4 q 1 Suppose a test charge q moves through the area with many fixed charges around q 6 q 3 q 2 q Since the distance from this charge to other charges changes, the potential energy changes PE elec k qq 1 qq 2... q q 1 2 q q r 1 r 2 r 12 r 13 The changes in potential energy are proportional to that charge Electric potential V: electric potential energy per unit charge: V PE elec q Units: J/CV (Volt) Phys 221 Spring 2014 Lecture 04 10

11 Electric Potential vs Electric Potential Energy Electric Potential is a property of an electric field and is measured in J/C or V Electric Potential Energy is an energy of system consisting of the charged object and the external electric field, and is measured in Joules. *Electric potential energy PE elec electric potential (or potential) V Phys 221 Spring 2014 Lecture 04 11

12 Potential Difference The potential difference between two points is the negative of the work done by the electrostatic force to move a unit charge from one point to another. Phys 221 Spring 2014 Lecture 04 12

13 Potential & Electric Fields The electric field points in the direction in which the potential decreases most rapidly. PE W Fx qex V PE q Ex V Ex E V E V x x V ˆx, y V ŷ, z ẑ Phys 221 Spring 2014 Lecture 04 13

14 Potential Difference The potential difference between two points is the negative of the work done by the electrostatic force to move a unit charge from one point to another. V V B V A PE q W q A B Phys 221 Spring 2014 Lecture 04 14

15 Potential Difference *independent of path *independent of test charge To find V, find work done on a positive charge q o by the electric field as it moves from i to f. i E At any point, the work done on the particle by electrostatic force: θ x f Potential Difference: W elec = q 0 E cos Δx The potential energy is: PE W elec q 0 E cos x V f V i PE q 0 E cos x Phys 221 Spring 2014 Lecture 04 15

16 Potential due to a point charge: V in space around a charged particle relative to the zero potential at infinity: For a point charge V(r) to V q 4 0 r V(r 0) r Phys 221 Spring 2014 Lecture 04 16

17 Potential due to a Group of Point Charges Find the Potential at the center of the square. N V(r) V n (r) 1 n1 4 o N n1 q n r n Principle of superposition q 1 = 12 nc q 2 = -24 nc - r 1 r 2 r 3 q 3 =31 nc q 4 =17 nc r 4 Phys 221 Spring 2014 Lecture 04 17

18 Electric Potential and Electric Field Calculate Electric Potential from the Electric Field V Ex Calculate Electric Field from the Electric Potential E V x Phys 221 Spring 2014 Lecture 04 18

19 Potential Energy Gravitational Potential Energy m m r Electric Potential Energy F e k q q F g G 2 2 PE G m 1 m 2 r U=0 at r = Potential energy: can be positive or negative Field force pushes a system to a configuration with lower potential energy: Field force does work on a system, leading to a decrease in its potential energy. But, the total energy is conserved, if there are no other forces. Phys 221 Spring 2014 Lecture r PE k q 1 q 2 r

20 BB i>clicker question An electron moves a distance of 1.5 m through a region where the electric field E is constant and parallel to the displacement. The electron s potential energy increases by J. What is the magnitude of E? E V x PE qx Nm C a) 3.1 N/C b) N/C c) 2.0 N/C d) J e) N/C e = C 1.5m k = Nm 2 /C 2 0 = C 2 /(Nm 2 ) 2N / C Phys 221 Spring 2014 Lecture BB

21 Equipotentials Definition: locus of points with the same potential. General Property: The electric field is always perpendicular to an equipotential surface. Phys 221 Spring 2014 Lecture 04 21

22 Equipotentials Phys 221 Spring 2014 Lecture 04 22

23 E due to an infinite line charge Corona discharge around a high voltage power line, which roughly indicates the electric field lines. Phys 221 Spring 2014 Lecture 04 23

24 Equipotential Surface: Examples Point charge infinite positive charge sheet electric dipole Phys 221 Spring 2014 Lecture 04 24

25 Potential inside & outside a conducting sphere V ref 0 at r. Common mistake: thinking that potential must be zero inside because electric field is zero inside. Phys 221 Spring 2014 Lecture 04 25

26 Demo PE q V Get energy out charge flow R V kq R r 1 r 2 V V(r 1 ) V(r 2 ) across fluorescent light bulb Phys 221 Spring 2014 Lecture 04 26