# Electrostatics III Pt II

 Calculating the Electric Potential  Knowing the potential energy, we can calculate the electric potential of a charge q at a point using what equation? V = Ue/q The parallel-plate capacitor creates a uniform electric field (state the formula)  The plates have area A and separation d. Let Ue = 0 when a mobile charge q is at the negative plate (x = ___). The charge's potential energy at any other position x is then the amount of work necessary to move the charge from the ______ ______ to that position  The hand does work on q to move it ______ against the field, thus giving the charge electric potential energy E = Q/ε0A(x = 0)negative plate uphill The hand push the charge q towards the positive plate at a constant speed. Thus, Fhand = ____ = ____ State the formula for the work to move the charge to position x:  W (2) State the formula for the work to move the mobile charge to position x within the contex of potential energy:  W (2) Fhand = Fe = qEW = (force)(displacement) = (Fhand)(x) = (qE)(x)W = ΔK + ΔUe = (qE)(x) The electric potential of the parallel-plate capacitor at position x, measured from the negative plate (Ue = ___, V = ___), is:  State the formula for V (3) The electric potential increases linearly from the ______ plate (x =  ___) to the ______ plate at (x = ___) The potential difference ΔVc between the two capacitor plates is:  ΔVc = _______ = _____  (Ue = 0, V = 0)V = Ue/q = Ex = (Q/ε0A)(x)negative plate (x = 0)positive plate (x = d)ΔVc = V+ - V- = Ed A 2-D equipotential map is represented below. The green dashed lines are _________ lines or simply _________.  equipotential linesequipotential  See notes To find the electric potential due to a single fixed charge q, we first find the electric potential energy when a second charge q' is a distance rB away from q ΔUe = ______ Take (Ue)A = 0 to be at a point infinitely far from q (i.e. rA → ∞) for convenience. This is a good reference point as the influence of the point charge q goes to _____ as we get _____ far from the charge ΔUe = Wby the handzero infinitely The force on q' gets larger as it approaches q. Thus, work done is not by a constant force and cannot use the equation W = Fd to find the work for a ______ ______ q' moving charge q' An exact calculation finds the electric potential energy of two point charges separated by distance r is:  Ue = ______ In the case where q and q' are opposite charges, the potential energy of the charges is _______. q' _______ toward fixed charge q. Uelec = 0 when q' is ______ far from q. As q' approaches q it gains ______ energy and loses ______ energy The y-axis is Uelec Ue = (ke)(qq'/r)negative accelerates infinitely kinetic energypotential energy For a charge q' that is a distance r from a charge q, the electric potential is related to the potential energy by V = ____.  The electric potential at distance r from a point charge q is:  V = ____ = ____ = ____ Only the source charge appears in this expression. (The source charge creates the _______ _______ around it) potential energyV = Ue/q' electric potential Electric potential at distance r from a point charge q Restate the formulas for V(3)   C. assume charges are positive unless told otherwise. Potential at point A: VA = keQ/rAPotential at point B: VB = keQ/rBVB/VA = (keQ/rB)(rA/keQ) = rA/rB = (1mm/3mm) = 1/3 The electric potential at a distance r > R from the center of a sphere of radius R and with charge Q is the same as the _____ _____ at a distance r from a point charge. electric potential The potential V0 is the potential at the surface of the charged sphere V0 = _____ = _____ The charge for a sphere of radius R is therefore:  Q = _____ The potential outside a charged sphere:  V = ______ = _______ = _____ The potential ______ _____ with distance from the center  D. V = keQ/r = (R/r)(V0)V0= [(V)(r)]/(R) = (30*15)/5 = 90V Check notes V is constant everywhere on the surface of a charged conductor in equilibrium. ΔV = ___ between any two points on the surface. No work is required to move a _____ _____ between any two points on the surface. The surface of any charged conductor in electrostatic equilibrium is an ________ ______. Why is it that the electric potential is constant everywhere inside the conductor and equal to the value at the surface. ΔV = 0test particle equipotential surfaceBecause the electric field is zero inside the conductor Consider a solid metal conducting sphere, Radius is R, total charge is Q. The electric potential is a function of ____. The electric field is a function of ____ r r2 Suppose there are many source charges, q1, q2... the electric potential V at a point in space is the ____ of the _______ due to each charge. So V = _____ = _____ Define ri   The electric potential is a simple _____ ____ which is easier to find sum of the potentials ri: the distance from charge qi to the point in space where the potential is being calculated scalar sum Label the diagram  (4)   B and D check notes Vector E and V are not two distinct entities, but instead, two different perspectives or two different mathematical representations of? Vector E at a point is _______ to the equipotential surface at that point  Vector E points in the direction of _______ potential Two different perspectives or two different mathematical representations of how source charges alter the space around themperpendiculardecreasing Vector E is ______ to the equipotential surface everywhere. Vector E points ______ in  the direction of ______ V. The field strength is ________ ________ to the spacing d between the equipotential surfaces perpendiculardownhill decreasing inversely proportional A positive charge speeds up as it moves from ______ to ______ potential. The work required to move a charge, at a ______ _____, in a direction opposite the electric field is:  W = ______ = _____ = _____ Constant speed → Fhand = ____ = ____ Thus = ____ (explain d) higher to lower potential constant speed W = Fhand = ΔUe = qΔVFhand = Fe = qE , where d is the distance between the two equipotential surfaces D. ΔU = eΔV = e(100V) = 100 eV Below are the three important arrangements of charges. Both electric field lines and equipotentials are shown. Remember the electric field vector is ______ to the equipotential surface.  In point charges and electric dipoles, field lines are everywhere _________ to equipotentials. The electric field is _______ where the equipotentials are closer together. For electric dipoles in a Parallel-plate capacitor, field lines point from ______ to ______ potential. For the capacitor, the field is ______ and so the equipotential spacing is _______ perpendicular perpendicular stronger higher to lower potential uniform constant  E field always points from high to low so possibly B E CAs the E Field goes up, the distance between the lines gets smaller and smaller so C A: Ans = B Distance is the shortest so E field is the strongest B: Ans = DC and D check notes Properties of a conductor in electrostatic equilibrium:  1. All excess charge is on the ______ 2. The electric field inside is ______ 3. The exterior electric field is ______ to the surface  4. The electric field strength is largest at the ______ ______ surfacezeroperpendicular sharp corners  Wire makes it so the potential is the same in both spheres. v1 = kQ1/r1v2 = kQ2/r2so:Q1/r1 = Q2/r22nC/1cm = Q2/2cmQ2 = 4 nC The electrical activity of cardiac muscle cells makes the beating heart an ______ ______. A resting nerve cell is _______; the outside is ______ and the inside is ________. Initially, all muscle cells in the heart are polarized, until an electrical impulse from the heart triggers the cells to ______, moving ions through the cell wall until the outside becomes ______. This causes the muscle to contract electric dipolepolarizedpositivenegativedepolarizenegative The depolarization of one cell triggers a wave of ________ to spread across the tissues of the heart. At any instant, a boundary divides the negative charges of _______ cells from the positive charges of cells that have not yet ________ in the heart. This separation of charges creates an electric dipole and produces a ______ ______ field and ______ depolarization depolarized depolarizeddipole electric field and potential The boundary between polarized and depolarized cells sweeps rapidly across the atria. At the boundary there is a charge separation. This creates an ______ ______ and an associated dipole moment  Label the diagram electric dipole A measurement of the electric potential of the heart is an invaluable diagnostic tool. The potential difference in a patient is measured between several pairs of ________. A chart of the potential differences is the __________, also called an _____ or an _____. With each heart beat, the wave of depolarization moves across the heart muscle. The dipole moment of the heart changes _______ and _______ electrodeselectrocardiogramECG or an EKGmagnitude and direction The records of the potential difference between the two electrodes is the ________.  The potential differences at a, b, and c correspond to those measured in the three stages shown to below electrocardiogram Authorchikeokjr ID346654 Card SetElectrostatics III Pt II DescriptionElectrostatics III Pt II Updated2019-04-24T20:25:34Z Show Answers