Chapter 23Electric PotentialDr. Ray KwokSJSUElectric Potential - Dr. Ray KwokGoals for Chapter 23• To study and calculate electrical potential energy• To define and study examples of electric potential• To trace regions of equal potential as equipotential surfaces• To find the electric field from electrical potentialElectric Potential - Dr. Ray KwokElectrical Potential Energy similar to gravitational, electrostatic force is a conservativeforce which means there is a potential energy associated with this force such that221e221GrqqkFrmmGF==0dFWnet=⋅=∫lrrdxdUF −=Gravitational forceCoulomb forceor gradient in 3DElectric Potential - Dr. Ray KwokWork and Potential Energy There is a uniform field between the two plates As the charge moves from A to B, work is done on it W = Fd = q Ex(xf– xi) ∆PE = - W= - q Ex∆x Only for a uniform fieldElectric Potential - Dr. Ray KwokPotential Difference (voltage) Potential difference is not the same as potential energy The potential energy and the potential difference are related by : ∆PE = q ∆V Both electric potential energy and potential difference are scalar quantities Units of potential difference V = J/C A special case occurs when there is a uniform electric field ∆V = VB– VA= -Ex∆x Gives more information about units: N/C = V/mElectric Potential - Dr. Ray KwokEquipotential Contour (2D)On a contour map, the curves mark constant elevation; the steepest slope is perpendicular to the curves. The closer together the curves, the steeper the slope.Electric Potential - Dr. Ray KwokEquipotential Surfaces (3D) An equipotential surface is a surface on which all points are at the same potential No work is required to move a charge at a constant speed on an equipotential surface The electric field at every point on an equipotential surface is perpendicular to the surfaceElectric Potential - Dr. Ray KwokEquipotentials and Electric Fields Lines – Positive ChargeThe equipotentials for a point charge are a family of spheres centered on the point charge The field lines are perpendicular to the electric potential at all pointsElectric Potential - Dr. Ray KwokFor two point chargesElectric Potential - Dr. Ray KwokApplication – Electrostatic Precipitator It is used to remove particulate matter from combustion gases Reduces air pollution Can eliminate approximately 90% by mass of the ash and dust from smoke Recovers metal oxides from the stackElectric Potential - Dr. Ray KwokElectric Potential of Point ChargesThe difference in potential energy between points A and B isBoAoBAAoBoABAoBoBA2orqqkrqqkUUrqqkrqqk)UU(rqqkrqqkUdrrqqkrdFW−=−+−=−−+−=∆−=⋅=∫∫rrElectric Potential - Dr. Ray KwokThe Electric Potential of a Point Chargeshown here is V for a positive and negative charge.PE between 2 pt charges:Electric potential from 1 pt charge:rqkVrqqkU21==Electric Potential - Dr. Ray KwokPotential energy curves—PE versus rU > 0 for like charges.U < 0 for opposite charges.F = - dU/drrqqkU21=Electric Potential - Dr. Ray KwokThe Electric Potential of Point ChargesThe electric potential of a group of point charges is the algebraic sum of the potentials of each charge.Electric Potential - Dr. Ray KwokHuman – a complex circuit?ECGAn electrocardiograph plots the heart’s electric potentialElectric Potential - Dr. Ray KwokEEGAn electroencephalograph measuresthe electrical activity of the brain.Electric Potential - Dr. Ray KwokThe Electron Volt The electron volt (eV) is defined as the energy that an electron gains when accelerated through a potential difference of 1 V Electrons in normal atoms have energies of 10’s of eV Excited electrons have energies of 1000’s of eV High energy gamma rays have energies of millions of eV 1 eV = 1.6 x 10-19JElectric Potential - Dr. Ray
View Full Document