Physics 212 Lecture 6, Slide 1Physics 212Lecture 6Today's Concept:Electric PotentialDefined in terms of Path Integral of Electric FieldPhysics 212 Lecture 6MusicWho is the Artist?A) John PrineB) Little FeatC) Taj MahalD) Ry CooderE) Los LobosWhy?Last time did Buena Vista Social Club (Cuba)Ry Cooder was the guy who brought them to our attention in this countryAlso, this album is great…. NOTE: Ellnora starts tonight…..Physics 212 Lecture 6, Slide 3Your Comments05“I'm pretty sure my head just exploded. Just... everywhere.”“help! i need somebody help! not just anybody help! you know i need someone HELLPP"“That last one was a doozy. Equipotential lines seem like they hold the key to something, but I don't know what yet.”“Do we have to be able to use/do problems with gradients?”“Are we going to differentiate the electric potential in three dimensions in order to get the electric field?”“The calculations with the spherical insulator were hard to follow. And I understand simple ideas, but I hope that the lecture helps me understand more fully.”Electric potential is related to energy – a key aspect of E’nM.We will use electric potential extensively when we talk about circuits.We really only need to know about derivatives (partial derivatives in a few cases).See example at end of class.Not too bad. After discussion today, I understand Gauss's Law!Physics 212 Lecture 6, Slide 4BIG IDEA• Last time we defined the electric potential energy of charge q in an electric field:40∫ ∫⋅−=⋅−=∆→bababaldEqldFU•The only mention of the particle was through its charge q. • We can obtain a new quantity, the electric potential, which is a PROPERTY OF THE SPACE, as the potential energy per unit charge. ∫⋅−=∆≡∆→→bababaldEqUV•Note the similarity to the definition of another quantity which is also a PROPERTY OF THE SPACE, the electric field. qFE≡Physics 212 Lecture 6, Slide 5Electric Potential from E field• Consider the three points A, B, and C located in a region of constant electric field as shown.40• What is the sign of ∆VAC= VC- VA ?(A) ∆VAC< 0 (B) ∆VAC= 0 (C) ∆VAC> 0 • Remember the definition:∫⋅−=∆→CACAldEV• Choose a path (any will do!)D∆x∫∫⋅−⋅−=∆→CDDACAldEldEV00 <∆−=⋅−=∆∫→xEldEVCDCAWhen you integrate 0, you get 0, everywhere.Physics 212 Lecture 6, Slide 6Checkpoint208ABD• Remember the definition∫⋅−=∆→BABAldEV0=∆→BAVV is constant !!0=EWhen the electric field is zero in a certain region, the electric potential is surely zero in that region. However it is not certain that the electric potential is zero elsewhere.Suppose the electric field is zero in a certain region of space. Which of the following statements best describes the electric potential in this region of space?A. The electric potential is zero everywhere in this regionB. The electric potential is zero at at least one point in this regionC. The electric potential is constant everywhere in this regionD. There is not enough information to distinguish which of the answers is correctThe potential is the integral of E dx. If E is zero then when you integrate you will just get a constant.Physics 212 Lecture 6, Slide 7E from V• If we can get the potential by integrating the electric field:40• We should be able to get the electric field by differentiating the potential?? ∫⋅−=∆→babaldEVVE ∇−=• In Cartesian coordinates: xVEx∂= −∂yVEy∂= −∂zVEz∂= −∂Physics 212 Lecture 6, Slide 8Checkpoint1a08• How do we get E from V??Look at slopes !!!VE ∇−=∂∂xVE = -x“The highest electric potential also means the greatest electric field.““The slope is the steepest there““The field and the potential are inversely related“The electric potential in a certain region is plotted in the following graph:At which point is the magnitude of the E-field greatest?A. B. C. D.Physics 212 Lecture 6, Slide 9Checkpoint1b08ABCD• How do we get E from V??Look at slopes !!!VE ∇−=∂∂xVE = -x“Because B is along the negative slope on the graph.““The slope of the electric potential at point C is positive“The electric potential in a certain region is plotted in the following graph:At which point is the direction of the E-field along the negative x-axis?A. B. C. D.Physics 212 Lecture 6, Slide 10Equipotentials• Equipotentials are the locus of points having the same potential40Equipotentials produced by a point chargeEquipotentials are ALWAYS perpendicular to the electric field linesThe SPACING of the equipotentials indicates The STRENGTH of the electric fieldPhysics 212 Lecture 6, Slide 11Checkpoint3a08ABCD“The field lines are dense at points A, B, and C, which indicates that the field is strong. However the lines are very spread out at D, indicating that the field is weakest there..“The field-line representation of the E-field in a certain region of space is shown below. The dashed lines represent equipotential lines.At which point in space is the E-field weakest?A. B. C. D.Physics 212 Lecture 6, Slide 12Checkpoint3b08ABCDABCD“The equipotential is weaker in the region between c and d than in the region from a to b.““The work is directly proportional to the distance between two charges. The distance between C and D is further away from that of A and B.” “The charge would have to cross the same number of equipotential lines regardless, so the change in potential energy is the same and therefore the work is the same.“The field-line representation of the E-field in a certain region of space is shown below. The dashed lines represent equipotential lines.Compare the work done moving a negative charge from A to B and from C to D. Which move requires more work?A. From A to B B. From C to DC. The same D. Cannot determine without performing calculationPhysics 212 Lecture 6, Slide 13HINT08ABCDELECTRIC FIELD LINES !!What are these ?EQUIPOTENTIALS !!• What is the sign of WAC= work done by E field to move negative charge from A to C ?(A) WAC< 0 (B) WAC= 0 (C) WAC> 0 A and C are on the same equipotentialWAC= 0 !!Equipotentials are perpendicular to the E field: No work is done along an equipotentialThe field-line representation of the E-field in a certain region of space is shown below. The dashed lines