Physics 2102 Jonathan Dowling Physics 2102 Lecture 06 THU 04 FEB Electric Potential I QuickTime and a decompressor are needed to see this picture Danger Volume m3 R R d 3 dR 4 R 3 Circle L Area m2 4 R 2 R 2 R L Circumference m Sphere d dR 2 R L R L 2 2 RL Cylinder Electric Potential Energy Electric Potential Energy U is Negative of the Work W to Bring Charges in From Infinity U W The Change in Potential Energy U Between an Initial and Final Configuration Is Negative the Work W Done by the Electrostatic Forces U Uf Ui W Q What is the potential energy of a single Q charge What is the potential energy of a dipole A proton moves from point i to point f in a uniform electric field as shown Does the electric field do positive or negative work on the proton Does the electric potential energy of the proton increase or decrease a Q Electric Potential Electric potential difference between two points work per unit charge needed to move a charge between the two points V Vf Vi W q U q r r dW F ds r r dW q0 E ds r r W dW q0 E ds f f i i r r W V V f Vi E ds q0 i f Electric Potential Energy Electric Potential Units Potential Energy U J Joules Electric Potential V U q J C Nm C V Volts Electric Field E N C V m Volts per meter Electron Volt 1eV Work Needed to Move an Electron Through a Potential Difference of 1V W q V e x 1V 1 60 10 19 C x 1J C 1 60 10 19 J Equipotential Surfaces r r W V V f Vi E ds q0 i f The Electric Field is Tangent to the Field Lines Equipotential Surfaces are Perpendicular to Field Lines Work Is Needed to Move a Charge Along a Field Line No Work Is Needed to Move a Charge Along an Equipotential Surface Electric Field Lines Always Point Towards Equipotential Surfaces With Electric Field Lines and Equipotential Surfaces Why am I smiling I m About to Be Struck by Lightning http www cco caltech edu phys1 java phys1 EField EField html Electric Potential and Electric Potential Energy The change in potential energy of a charge q moving from point i to point f is equal to the work done by the applied force which is equal to minus the work done by the electric field which is related to the difference in electric potential U U f U i Wapp W q V We move a proton from point i to point f in a uniform electric field as shown Does the electric field do positive or negative work on the proton Does the electric potential energy of the proton increase or decrease Does our force do positive or negative work Does the proton move to a higher or lower Example Consider a positive and a negative charge freely moving in a uniform electric field True or false a Positive charge moves to points with lower potential b Negative charge moves to points with lower potential c Positive charge moves to a lower potential energy d Negative charge moves to a lower potential energy a True b False c True d True Q V Q 0 V Conservative Forces The potential difference between two points is independent of the path taken to calculate it electric forces are conservative r r W U V V f Vi E ds q0 q0 i f Electric Potential of a Point Charge P r r V E ds E ds f i R R kQ kQ kQ 2 dr r r R Note if Q were a negative charge V would be negative Electric Potential of Many Point Charges Electric potential is a SCALAR not a vector q4 Just calculate the potential due to each individual point charge and add together Make sure you get the SIGNS correct qi V k ri i r3 r4 q5 r5 Pr2 q2 r1 q1 q3 Electric Potential and Electric Potential Energy U Wapp q V Q a What is the potential energy of a dipole Q Q a Q First Bring charge Q no work involved no potential energy The charge Q has created an electric potential everywhere V r kQ Second The work needed to bring the charge Q to a distance a from the charge Q is Wapp U Q V Q kQ a kQ2 a The dipole has a negative potential energy equal to kQ2 a we had to do negative work to build the dipole electric field did positive work Positive Work Q a Q Negative Work Q a Q Positive Work Charge Moves Uphill QuickTime and a decompressor are needed to see this picture Q a Q Negative Work Q a Q Charge Moves Downhill Potential Energy of A System of Charges 4 point charges each Q and equal mass are connected by strings forming a square of side L If all four strings suddenly snap what is the kinetic energy of each charge when they are very far apart Use conservation of energy Final kinetic energy of all four charges initial potential energy stored energy required to assemble the system of charges Q Q QuickTime and a decompressor are needed to see this picture Q Q Let s do this from scratch Potential Energy of A System of Charges Solution Q No energy needed to bring in first charge U1 0 L Energy needed to bring in 3rd charge kQ 2 kQ 2 U 3 QV Q V1 V2 L 2L Energy needed to bring in 4th charge 2kQ 2 kQ 2 U 4 QV Q V1 V2 V3 L 2L Q 2L Energy needed to bring in 2nd charge kQ 2 U 2 QV1 L Q Q potential energy is sum Total of all the individual terms shown on left hand side 2 kQ 4 2 L So final kinetic energy of each charge 2 kQ 4 2 4L Example qi V k ri i Positive and negative charges of equal magnitude Q Q Q are held in a circle of radius R 1 What is the electric potential at the center of each circle VA VB VC k 3Q 2Q r kQ r k 2Q 4Q r 2kQ r k 2Q 2Q r 0 A 2 Draw an arrow representing the approximate direction of the electric field at the center of each circle B 3 Which system has the highest electric potential energy C UB Q Vb has largest un canceled charge Electric Potential of a Dipole on axis What is V at a point at an axial distance r away from the midpoint of a dipole on side of positive charge V k Q k Q a a r r 2 2 a a r 2 r 2 kQ a a r r 2 2 Qa 2 a 4 0 r 2 4 p a Q Q r Far away when r a p V 4 0 r 2 Electric Potential on Perpendicular …
View Full Document
Unlocking...