22ElectricPotential22电动势

Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,*,*,22.Electric Potential,Topics,Recap:Potential Energy,Electric Potential Difference,The Volt and the,Electronvolt,The Potential of a Point Charge,Potential Difference from Superposition,Electric Field from Electric Potential,Charged Conductors,2,Recap:Potential Energy,The,work,done by a force along a path from point,A to point B is defined by,3,Recap:Potential Energy,If the force is,conservative,we can define,the,potential energy difference,as follows:,The potential energy difference,D,U,depends only,on the end points A and B,that is,it is,independent of the path,taken between A and B.,4,Electric Potential Difference,Electric Potential Difference,Suppose a charge+,q,is moved from A to B against,a,uniform,electric field.The,change,in potential energy is,The potential energy is,increased,.,6,Electric Potential Difference,The,electric potential difference,between two points,A and B is defined as,the energy per unit charge,:,For the special case of a uniform electric field,we,can write:,A,B,7,The Volt and the,Electronvolt,The electric potential difference between two points,is such an important idea that it is given its own unit:,the,volt,(V).If a charge moves,over an electric potential,difference of,D,V,volts,the,potential energy,changes,by,D,U,=,q,D,V,.,Example,:A 12-V car battery does 12 J of work,in moving 1 C of charge from one battery terminal,to the other.,A,B,8,The Volt and the,Electronvolt,Some Electric Potential Differences,Between arm and leg 1 mV,Across cell membrane 80 mV,Car battery 12 V,Electric outlet 100 240 V,Between power line and ground 365 kV,Between base of thundercloud 100 MV,and ground,9,The Volt and the,Electronvolt,For molecular and atomic systems,it is usually more convenient to measure energy in,electronvolts,(,eV,).(This is not an SI unit!),One,electronvolt,is the energy gained by a particle carrying one elementary charge when it moves through a potential difference of 1 volt,.,Example,:the ionization energy of hydrogen is,13.6,eV,.,Since the value of an elementary charge is 1.6 x 10,-19,C,1,eV,is,1.6 x 10,-19,J,10,Example:A Power Line,A long straight power-line wire,of radius,r,=1.0 cm with charge density,l,=2.6,m,C/m,is at a height,h,=22 m above the ground.,What is the potential difference,D,V,between the cable and the ground,assuming that the electric field is,approximately that of a line charge?,h,D,V,11,Example:A Power Line,We found that the electric field of an infinitely,long line charge is given by,h,D,V,where the unit vector is perpendicular,to,and points away from,the wire.,The potential difference is,that is,360 kV,12,Potential of a Point Charge,The Potential of a Point Charge,Consider a positive point charge.The,change,in,electric potential between points A and B is,given by,This shows that if a positive charge,moves from A to B the potential,energy,decreases,14,The Potential of a Point Charge,Although only changes in potential are physically,relevant,it is often convenient to,choose,the location,of the,zero,of the potential.For,a car battery,this is typically the cars,chassis;for an electrical outlet it,is the ground.For an isolated point,charge,it is convenient to choose,the potential to be,zero at infinity,15,The Potential of a Point Charge,The potential difference between two points,A and B from a point charge,can be re-written as,When,r,A,=,infinity,the last,term vanishes.We are free to,choose,V,(,A,)as we please,e.g.,V,(,A,),=,0,.,16,The Potential of a Point Charge,With this choice,the potential of a point charge,becomes,Remember,however,that only,differences,in this number are,physically relevant because we,can always add to it an arbitrary,constant without altering the physics,17,Potential Differences using Superposition,+,-,+,+,+,-,-,The potential at a given point,is the sum,of the electric,potentials,due to every,point charge,Electric Potential of a Collection of Charges,19,The electric potential for a charge distribution is,given by a formula similar to that for an electric field,Electric Potential for a Charge Distribution,But unlike the electric field the electric potential,is a,scalar,20,x,Example A Charged Ring,Note:for a fixed point P,the distance,r,is constant as we integrate around,the ring.,Therefore,21,x,x,2,Example A Charged Disk,The potential for a ring of charge,is,Therefore,for a disk we can write,22,x,x,2,Example A Charged Disk,The charge on a ring of radius,a,is,where,s,is the,surface charge,density.,Therefore,23,x,x,2,Example A Charged Disk,After performing the integral,we obtain,24,Equipotentials,If one draws a surface through all points with the same potential,one obtains an,equipotential,.,Here,for example,are,some,equipotentials,for,a dipole,25,Electric Field from Electric Potential,Electric Field fromElectric Potential,Since,one can compute the electric field from the potential,V,using the,gradient,:,This is the gradient,