Week 3 Day 2 What is the de nition of electric potential What is the de nition of electric potential energy The difference between two points A and B as the change in potential energy per test charge in moving a test charge from A to B Units Volts Negative of the work done by conservative forces Units Joules We can describe the energy properties of the eld independently of the energy of some particular object located in the eld What is the relation between them Suppose an object with charge q is moved across a potential difference V The change in the potential energy of the object is then U q V Concept Question Motion of Charged Object in an Electric Field Correct answer 2 A charged point like object is released from rest in a statistic electric eld due to other xed charged sources Consider the system consisting of the charged objects and the sources of the xed electric eld At some time later the charged object will move to a new point in space such the potential energy of the system decreases independent of the sign of charge Electric Work Concept Question Sign of Work Electrically force on object 1 due to interaction between charged objects 1 and 2 Work done by electrical force moving object 1 from A to B Correct answer 3 A positively charged object charge q 0 is xed at the origin You move a negatively charged object charge q 0 from A to B with r r where r is the distance from the origin Work done by the electrostatic force is negative and you do a positive amount of work Group Problem Work done by Electrical Force A point like charged source object charge q 0 is held xed A second point like charged object charge q 0 is initially at a distance r from the xed source and moves to a nal distance r from the xed source What is the work done by the electrical force on the moving object Hint What coordinate system is best suited for this problem Group Problem Motion of an Electron Change in a Uniform Electric Field Consider two thin oppositely uniform charged thin plates separated by a distance d The surface charge densities on the plates are uniform and equal in magnitude An electron with charge e and mass m is released from rest at the negative plate and moves to the positive plate What is the speed of the electron when it reaches the positive plate Gaussian Symmetry Pillbox Apply superposition Potential Energy Difference Suppose a xed charged source charge qs is at the origin and a charged point like particle charge q1 moves from A toB with rA rB where r is the distance from the origin The change in potential energy due to the interaction is de ned to be the negative of the work done in moving the charged point like particle from A to B Potential Energy Zero Point Generalization Choose the zero point for the potential energy at in nity U 0 Then set r and r r The potential energy as a function of distance r from the source charge q is This is equal to the negative of the work done by the electrostatic interaction when a charged object moves from in nity to a distance r from the charged point like source particle Electric Potential Difference due to Source of Charge Change in potential energy per test particle in moving the test object charge q from A to B Units Joule Coulomb Volt Here we assume that the charged test particle does not effect the source Concept Question Motion of Charged Objects Correct answer 2 If you place a positively charged particle in an electric eld the charge will move from higher to lower electric potential resulting in an decrease in potential energy E Field and Potential Effects A charged particle charge q and mass m in an electrostatic electric eld will experience a force given by F qE When a charged particle charge q is moved across an electric potential difference then the change in potential energy is U q V The change in mechanical energy of the charged particle is W E K U m v v q V Con guration Energy What is the potential energy stored in a con guration of charged objects Start with all the charged objects at in nity Choose U 0 Bring in the rst charged object U 0 Bring in the second charged object U U k q q r Bring in the third charged object U U U k q q r k q q r Con guration energy U U U U k q q r k q q r k q q r Group Problem Stored Energy in Charge Con guration How much energy does it take you to assemble the charges into the con guration at left assuming they all started out an in nite distance apart Potential Created by Point Charge V V V E s E kq s r r r V kq s kq r r V kq Zero Point for Electric Potential Generalization Concept Question Continuous Charge Distribution Superposition Principle Potential Function Choose r and r r Choose V 0 Then the electric potential function at a point P a distance r from the point like charged source charge q is STOPPED HERE IN CLASS Correct answer The work done by the electrostatic interaction when a positively charged particle that starts from rest at in nity and is moved to the point P midway between two xed charges of magnitude Q and Q is Break distribution into in nitesimal charged elements of charge q Electric potential difference between in nity and P due to q is Calculating Electric Potential Difference for Continuous Distribution Choose V 0 Choose integration r Identify q s a v Choose eld point variables r Calculate source eld point distance r r De ne limits of integration Integrate Worked Example Uniformly Charged Ring Consider a uniformly charged ring with total charge Q Find the electric potential difference between in nity and a point P along the symmetric axis a distance z from the center of the ring Q 2 R and q s R Choose V 0 r Rr and r zk r r R z V V z V z Group Problem Uniformly Charged Rod A thin road extends along the z axis from x l to x l The rod carries a uniformly distributed positive charge Q Calculate the electric potential difference between in nity and at a point P along the x axis
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