Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Internal energy wikipedia , lookup
Field (physics) wikipedia , lookup
Electrical resistivity and conductivity wikipedia , lookup
Conservation of energy wikipedia , lookup
Anti-gravity wikipedia , lookup
Lorentz force wikipedia , lookup
Nuclear structure wikipedia , lookup
Introduction to gauge theory wikipedia , lookup
Aharonov–Bohm effect wikipedia , lookup
Potential energy wikipedia , lookup
Lecture 6-1 Thin sheet of any charge distribution tiny disk E ( E ' E disk ) ( E ' E disk ) E disk E disk n 2 0 2 0 n 0 E L E ' E disk Just to left of disk E R E ' E disk Just to right of disk E n 0 Lecture 6-2 Charges and fields of a conductor • In electrostatic equilibrium, charges inside a conductor do not move. Thus, E = 0 everywhere in the interior of a conductor. • Since E = 0 inside, there are no net charges anywhere in the interior. Net charges can only be on the surface(s). 0 The electric field must be perpendicular to the surface just outside a conductor, since, otherwise, there would be currents flowing along the surface. Lecture 6-3 Electrostatic Shielding (Continued) If you move charge q in the cavity, the exterior electric fields and the extreior charge distribution are not affected. q Conducting shell electrostatically shields its exterior from changes on the inside. Add Q’ Q’’ + + + + + + If you now add charge Q’ to the conductor and/or Q’’ on the outside of the conductor, the interior electric fields do not change. Conducting shell electrostatically shields its interior from changes on the outside, too. Lecture 6-4 READING QUIZ 1 IN WHAT DIRECTION CAN YOU MOVE A TEST CHARGE RELATIVE TO AN ELECTRIC FIELD SO THAT THE ELECTRIC POTENTIAL DOES NOT CHANGE? A| Move in the direction of the electric field lines. B| Move opposite to the direction of the electric field lines. C| Move from point A in the electric field to point B in in the electric field along an arbitrary path. D| Move relative to the electric field along a path which is everywhere perpendicular to the electric field. Lecture 6-5 Electric Potential Energy of a Charge in Electric Field • Coulomb force is conservative => Work done by the Coulomb force is path independent. dl • Can associate potential energy U (r ) to charge q0 at any point r in space. It’s energy! A scalar measured in J (Joules) dW q0 E d l dU dW q0 E d l Lecture 6-6 Electric Potential Energy of a Charge (continued) U U ( r ) U (i ) r 0 i qq00EE ddl l r i i is “the” reference point. Choice of reference point (or point of zero potential energy) is arbitrary. i is often chosen to be infinitely far () dl dW q0 E d l dU dW q0 E d l Lecture 6-7 Gravitational vs Electrostatic Potential Energy U U (b) U (a ) a bb FF d dl l aa b mg qE Gravity Coulomb mg l qE l (if g, E uniform) Work done by gravity or the Coulomb force decreases the potential energy. Lecture 6-8 Potential Energy in the Field due to a Point Charge q From ∞ U (r ) dl qq0 EE dl 0 PP q0 q k 2 r dl l P q0 q k 2 dl l r r q0 q q0 q k k r l This is also called the potential energy of the two-charge configuration of q and q0. What is the work required to bring q0 in from infinity? Lecture 6-9 Potential Energy of a Multiple-Charge Configuration (a) kq1q2 / d (b) q1q3 q2 q3 q1q2 k k k d d 2d (c) q1q3 q2 q4 q3q4 q1q2 k k k k d d d d q2 q3 q1q4 k k 2d 2d Lecture 6-10 Physics 241 –Warm-up quiz Three point charges carry the same charge -q. Which of the following statements is true? Select one of (a) – (e). -q -q -q A B A. An electron would have a higher potential energy at point A than at point B B. A proton would have a higher potential energy at point A than at point B C. An electron would have a lower potential energy at point A than at point B D. The potential energy is the same for an electron and a proton at point A. E. The potential energy is the same for a proton at point A and point B. Lecture 6-11 Electric Potential • U(r) of a test charge q0 in electric field generated by other source charges is proportional to q0 . • So U(r)/q0 is independent of q0, allowing us to introduce electric potential V independent of q0. U ( r ) V ( r ) q0 U (r) V (r) q0 • [Electric potential] = [energy]/[charge] SI units: J/C = V (volts) 1J taking the same reference point Scalar! Potential energy difference when 1 C of charge is moved between points of potential difference 1 V Lecture 6-12 Potential at P due to a point charge q From ∞ V (r ) U q0 (r ) q0 q k r Lecture 6-13 Electron Volt • V=U/q is measured in volts => 1 V (volt) = 1 J / 1 C J N m V E m V POTENTIAL C CDIFFERENCES V2 – V1 N V E C m 1 J 1C 1V 1 eV | e | 1V 1.602 1019 C 1V (electron volt) • V depends on an arbitrary choice of the reference point. • V is independent of a test charge with which to measure it. Lecture 6-14 DOCCAM 2 Lecture 6-15 Potential due to two (source) charges q1 q2 0 q1 q2 V ( x) k k |x| |xa| Lecture 6-16 Potential due to Multiple Source Charges: Example V ( P) q1 q2 q3 q4 k d/ 2 Dotted line is an equipotential when q1=12nC, q2= -24nC, q3=31nC, q4=17nC E from V We can obtain the electric field E from the potential V by inverting the integral that computes V from E: r r V (r ) E d l ( Ex dx E y dy Ez dz ) V Ex x V Ey y V Ez z Expressed as a vector, E is the negative gradient of V E V Lecture 6-18 Lightning E = 3 x 106 N/C at electrical breakdown of air ΔV on the order of 109 V http://micro.magnet.fsu.edu/electromag/java/lightning/index.html Lecture 6-19 DOCCAM 2 Examples (only a Preview) Q Point charge Q: V ( r ) k r Uniformly charged sphere: Q V ( r ) k r>R r r<R E (r ) k Q V r r 2 r r Q E (r ) k 2 r r Q r2 V (r ) 3 2 4 0 2 R R 1 1 Qr E (r ) r 3 4 0 R V z z (1 )z 2 2 z 2 0 z R Charged disk: V ( z ) ?? Charged sheet: V ( z ) ?? E ( z ) sgn( z ) V ( z ) ?? E (r ) r 2 0 r Charged line: E( z) z 2 0 Lecture 6-21 Physics 241 – 10:30 Quiz 3 A spherical shell is uniformly charged with a positive charge density σ. Which of the following statements is (are) true? Select one of (a) – (e). 1. An electron would have a higher potential energy at point A than at point B 2. A proton would have a higher potential energy at point A than at point B 3. The electric potential is lower at A than at B 4. The electric potential is higher at A than at B a) b) c) d) e) 1 and 3 only 1 and 4 only 2 and 3 only 2 and 4 only None of them σ A B Lecture 6-22 Physics 241 – 11:30 Quiz 3 A sphere is uniformly charged with a negative surface charge density. Which of the following statements is (are) true? Select one of (a) – (e). 1. A proton would have a higher potential energy at point A than at point B 2. An electron would have a higher potential energy at point A than at point B 3. The electric potential is lower at A than at B 4. The electric potential is higher at A than at B a) b) c) d) e) 1 and 3 only 1 and 4 only 2 and 3 only 2 and 4 only None of them -σ A B