General Physics Electricity and Magnetism
General Physics Electricity and Magnetism PHYS 212
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Date Created: 11/01/15
Ch ter 24 Electric Potential Relationship between Work done by a force and ENERGY If you accelerate an object to a greater speed by applying a force you increase its kinetic energy These changes in KE are due to energy transfers you transfer energy from yourself to the object you do work Definition of Work w i 11Mquot J Lw 1 u w J 39 Area 2 AA F1 Ax W0 rk x NV 1H 17 7 5 mud 1 1L g A a Work done raising an object of on a falling penguin is independent of path depends only on the e dpoints 0f m0ti0npri Can de ne a W n i s fn mg39dy y mg dv CONSERVATION OF MECHANICAL ENERGY lmv2m lmv2m 2 139 8y 2 f 83 K1 U1 2 Kf Uf E1 Ef Energy is Conserved for conservative forces Work Energy Theorem The work done by W 2 IF OR More Generally a resultant force 01 changes the kinetic 3 energy of an object dt dt dt fwd V var v0 d f 1 f 2 mJ lt vgtd lt gtd d 6 WR K KO t 2 mv v Work and ELECTRIC POTENTIAL Energy Energy considerations and the Electric Field Consider a point charge qo in an electric eld E Apply the definition of work Week dime fe a point charge moving in the presence of amethelr point charge Lime week elem memimgg A e H B Wq0JHd A f y A VL NM we B qu0 A47r80r w f thw Wig ka due 0 a mint m mg the fd dscos 9dr VB 1 W011 Juu wgl W q d r39rquotrwrquot3939r rh go 2 7 4725 r whence m r39mJ Jl39 0 r II 4 f It its time fm any arbitrary haurga dismimeme The Electric Potential Difference AV The electric force is conservative Potential energy can be de ned according to Divide by test charge to determine change in the potential energycharge AV Electric potential JoulesCoulomb 2 volts v Note the electric eld can now be expressed in voltsm NC Electric Potential of Point charges Potential energy of a point charge is referenced to zero no 1s chosen to be the zero point due to the potential energy s dependence on lr The tential at P due to several charges ma found by rst nding the due to ea charge and adding SUPERPOSITION The potential is a scalar and may be added algebraically for several charges Equipotential Surfaces consider case when path element d is J to E W E CE Eds cos 6 0 Eds cos90 Eid Equipotential and Field Limes Vv Continuous Charge Distribution and Calculating the ElectricField The electric potential difference for a continuous distribution of charge is found by integrating small increments of charge a A dV E s ds 7 The electric eld may be found by 8 ds reversing the process or differentiating a V a V R 6V oNote the mathematical operation is called 2 117 A nding the gradient K 6x 6y 2 The Electric P temtial Diffemmm if m m m B A 4 8 r r 7239 B A T713 Emlij39iml wra Nimrij tum Slhwtr JMJTQC B 0 VB VA j k d 28 A 0 23 039 VB VA 2 dz 28 r 0 2A 7 VBVA AZ V 2 g B A change from mming a charge in a unifmm eid E Rikquot quot n A A VB VA 2 Ed Comservamn 0f Energy lq VB VA qu W applied to m om of a qAV W 2 AK charge The Electron Volt A unit of enery is the electron volt which is de ned as the amount of energy an electronic charge gains when accelerated through a potential difference of one volt 16V 1602 x1049 J Equipotential and Field Lines Conductors Example of Con mtms 5 1 NL xx