Electrostatic Potential Energy and Electrostatic Potential 10 20 14 9 18 AM Works depend on initial point final point and path taken Conservative Forces Gravitational electrical Work done is independent of the path taken only depends on the final and initial points o Electrostatic Potential Energy Electrostatic Potential potential Useful to define another quantity electrostatic potential Example Units of V Joules per coulomb Volts F E are vector quantities while U and V are scalar F q E U q V W q E delta x delta U q delta V Potential of a point charge Potential Energy of Two Charges Multiple Charges o o o Calculate E given V 1 dimensional o o Example o 3 dimensional Point charge with radial symmetry o o V from charge distributions point charge Multiple charges o If you have several charges and want to find the potential at a certain point then you just add the potentials of the individual charges Continuous charge distribution o Example find the potential V along the axis of a ring of charge Q evenly distributed of radius a Use E dV dz and find E to see if it compares with result above Approximations Example Find V for a Uniform sphere of charge Q radius a uniformly charged inside and outside Inside sphere when r a Graph it Infinite Line Charge NOTE V final can t be V infinity because there is charge at infinity because the line charge is infinite so V infinity 0 CAN T BE EQUAL TO ZERO so you must set an arbitrary point to be zero potential its ok for it to be zero because its just relative to the other point Cylindrical Infinite Charge Homework exercise find potential for a finite line charge along y axis length 2a total charge Q find potential at a distance x along x axis perpendicular find potential dq and integrate over the line Potential for parallel sheets of charge surface charge density sigma and sigma distance d apart Potential energy of a charge between the two plates o Conductors and Equipotential Surfaces Equipotential surface any real or imaginary surface which is all at the same potential E field lines intersect equipotential surfaces at right angles perpendicular gradient is always in the direction of greatest increase ie 90 degrees o o Conductors are equipotential surfaces because the charge always flows to the outermost surface of a conductor and the electric field is always perpendicular to the conducting surface because horizontal component of electric field would move the charges around and we have decided that all the charges are motionless after a certain time o Therefore V constant on the surface of a conductor o No electric field on the inside of a conductor so it is equipotential Vi Vf therefore V constant Example find potential for a conducting sphere o In general with conductors Review for Exam One Exam 1 Revisit HW problems 10 20 14 9 18 AM Exam is similar to HW problems Equation sheet on a 3 x 5 note card both sides Review end of chapter summaries Three problems with parts Allowed a simple calculator trig functions but no graphing Can solve problems with 1 4 pi epsilon naught k 9 10 9 Electric field and potential of an infinite line charge by a perpendicular bisector Electric field and potential of a point charge Electric field and potential of a sphere Electric field and potential of a FINITE line charge Electric field and potential for a shell Finite Line Charge Going over the exam in class
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