Lecture 8 Electric Potential Chapter 25 Review Electric Potential Energy U U U f U i W Electric Potential V W U V V f Vi q q Electrostatic force is conserved work done by force is path independent Review Equipotential surface all points are at same potential E field lines are to the equipotential surface If given equipotential surfaces can draw E field lines Review From W V q and r r dW F d s Derived equation for finding a potential in a E field f V f Vi i r r E ds Potential always decreases if move along a path in the direction of the E field Electric Potential 18 Derive potential V around a charged particle V f Vi i f r r E ds Imagine moving a test charge from P to Path doesn t matter so choose line radially with E Electric Potential 19 Chose path so r r E ds E cos ds Eds Using radial path rewrite ds dr Use limits for i R and f V VR Edr R Electric Potential 20 Use E for point charge q E k 2 r Define V 0 1 0 V kq 2 dr R r Electric Potential 21 Finish integral q 1 0 V kq k R r R Letting R become any distance r from particle q V k r Electric Potential 22 Sign of V is same sign as q charge produces V charge produces V q V k r V gets larger as r gets smaller In fact V when r 0 on top of charge From shell theorem this holds outside or on external surface of a spherical charge distribution Electric Potential 23 What is the force F electric field E and potential V at a point P a distance r away from a point charge r q q0 F k 2 r r q E k 2 r q V k r Electric Potential 24 Use superposition principle to find the potential due to n point charges n n qi V Vi k i 1 ri i 1 This is an algebraic sum not a vector sum Include the sign of the charge Electric Potential 25 Checkpoint 4 Rank a b and c according to net electric potential V produced at point P by two protons Greatest first q q V k d D ALL EQUAL Electric Potential 26 Replace one of the protons by an electron Rank the arrangements now q q V k d D ALL EQUAL Electric Potential 27 Potential due to a dipole Sum V for 2 charges q q r r kq V Vi k i 1 r r r r 2 Usually far away from dipole so r d r r d cos r r r 2 Electric Potential 28 r r qd cos k V kq 2 r r r For dipole p qd p cos V k 2 r Measure from dipole axis to r Electric Potential 29 How do we calculate E from V W q0 V r r r r W F d qE d q0dV q0 E cos ds dV E cos ds Electric Potential 30 How do we calculate E from V dV E cos ds Component of E in direction of ds V Es s Component of E in any direction is neg rate of change of V with distance in that direction Electric Potential 31 Take s axis to be x y or z axes V V V Ex Ey Ez x y z If E is uniform and s is to equipotential surface V E s Electric Potential 32 Checkpoint 6 3 pairs of parallel plates with same separation and V of each plate E field is uniform between plates and to the plates A Rank greatest first magnitude of E between the plates Electric Potential 33 V E s 200 E1 d but asked for magnitude of E 220 E2 d 2 then 1 3 200 E3 d Electric Potential 34 Checkpoint 6 b For which pair does E point to the right 3 C If an electron is released midway between plates in 3 what does it do Accelerate to the left Electric Potential 35 Define electric potential energy U of a system of charges as to the W done by an external F to assemble the system bringing each charge from Bring q1 from W 0 since no electric F yet Bring q2 from Wapp q2V because q1 exerts electrostatic F on q2 during the move Electric Potential 36 Potential due to q1 is q1 V k r From definition of potential energy q1q2 U W q2V k r Charges of like sign W and U are Charges of opposite sign W and U are Electric Potential 37 What is the potential energy when add an additional charge to system Move q1 from W U 0 Move q2 from q1q2 W12 U12 k d Electric Potential 38 Now bring in q3 q1q3 W13 U13 k d Must also remember q2 q2 q3 W23 U 23 k d Electric Potential 39 Total potential energy is the scalar sum U U12 U13 U 23 q1 q q2 4q q3 2q 10q 2 q 4q q 2q 4q 2q U k k d d d d Electric Potential 40 Using what we know about conductors E 0 inside All excess charge is on surface All points of a conductor whether inside or on the surface are at the same potential A conductor is an equipotential surface
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