Presentation on theme: "Electric Potential Energy & Electric Potential Unit 8"— Presentation transcript:
1Electric Potential Energy & Electric Potential Unit 8
2Recall ‘Work’ from earlier Work done by a force is given by:W = F d cos(q) or+W: Force is in direction moved-W: Force is opposite direction movedW=0: Force is 90o to direction movedConservative ForcesDU = -WfieldUse book or brick for prop. Ask students if I am doing positive or negative work, what about gravity.
3Electric Potential Energy ΔU = -WfieldGeneral Points:1) Potential Energy increases if the particle moves in the direction opposite to the field force.Work will have to be done by an external agent for this to occur2) Potential Energy decreases if the particle moves in the same direction as the field force on it
4Electrical Potential Energy Graphical look at EPEThe potential energy is taken to be zero when the two charges are infinitely separated
5Potential Energy of a System of Charges Start by putting first charge in positionNo work is necessary to do thisNext bring second charge into placeNow work is done by the electric field of the first charge. This work goes into the potential energy between these two charges.Now the third & fourth charge are put into placeWork is done by the electric fields of the two previous charges.The total EPE is then given by (signs matter)
6ExampleA test charge is brought separately to the vicinity of a positive charge Q at pt BAqrQCharge +q is brought to pt A, a distance r from QBA(a) UA < UB(b) UA = UB(c) UA > UBI) Compare the potential energy of q to that of Q.(a)(b)(c)II) Suppose charge q has mass m and is released from rest from the above position (a distance r from Q). What is its velocity vf as it approaches r = ∞ ?
7Work Done by Uniform Electric Field Force on charge isWork is done on thecharge by field
8ELECTRIC POTENTIALConsider a ball of mass, m, placed at a point in space (height, h, above Earth). It would possess a certain PE per unit mass due to it being in the gravitational field of Earth.If the ball was replaced by a bowling ball of mass, M, it too, would possess the SAME potential energy per unit mass.
9Similarly, 2 different sized charges at the same distance from the charged sphere (green) will have the same EPE/charge.The electric potential energy per unit charge for some location in an electrical field is called electric potential.
10Electric PotentialElectric potential is defined as the potential energy per unit charge at a point in space
11Comparison: Electric Potential Energy vs. Electric Potential Electric Potential Energy (U) - the energy of a charge at some location.Electric Potential (V) - tells what the EPE would be if a charge were located there
12Voltage and Potential Energy Positive charge will naturally move towards lower electrical potential energies, lower voltage.
13General Points for either positive or negative charges: Positive potential is taken to be higher by definition due to positive test charge.
14Relation between Potential and Field The work done by the electric field force in moving a charge from point a to point b is given by
15Electric Potential for a Point Charge The direction of the electric field from a point charge is always radial. We integrate from distance r (distance from the point charge) along a radial line to infinity:
16What is the electric potential difference between A and B?
17Rank (a), (b) and (c) according to the net electric potential V produced at point P by two protons. Greatest first.A: (b), (c), (a)B: all equalC: (c), (b), (a)D: (a) and (c) tie, then (b)
18Question… The electric potential at point A is _______ at point B greater thanequal toless than
19Points A, B, and C lie in a uniform electric field. 1) If a positive charge is moved from point A to point B, its electric potential energya) Increases b) decreases c) doesn’t change2) Compare the potential differences between points A and C and points B and C.a) VAC > VBC b) VAC = VBC c) VAC < VBC
20Two ChargesIn region II (between the two charges) the electric potential is1) always positive2) positive at some points, negative at others.3) always negativeIIIIIIQ=+7.0mCQ=-3.5 mC
21Potential for two charges Calculate electric potential at point A due to chargesA4 m6 mHow much work do you have to do to bring a 2 mC charge from far away to point A?Q=+7.0mCQ=-3.5 mC
22Potential of a solid conducting sphere (radius R) with charge +Q Find V at the following locations:+Qi) At r > RRii) at r = R
28Equipotential (EP) Surfaces & Their Relation to Electric Field An equipotential surface is a surface on which the electric potential is the same everywhere.The EP surfaces that surround the point charge +q are spherical. The electric force does no work as a charge moves on a path that lies on an EP surface, such as the path ABC.However, work is done by the electric force when a charge moves along the path AD.
29Equipotential Surfaces & Their Relation to Electric Field Equipotential surfaces (in blue) of an electric dipole. The surfaces are drawn so that at every point they are perpendicular to the electric field lines (in red) of the dipole.The radially directed electric field of a point charge is perpendicular to the spherical equipotential surfaces that surround the charge. The electric field points in the direction of decreasing potential.
30Consider two conducting spheres with differing radii Ra and Rb sitting on insulating stands far apart. The sphere with radius Ra has an electric charge +Q. If we connect a thin, conducting line between the spheres, then disconnect it, what are the charges on the spheres?
312 identical spheres question +Q +Q/ higher V?Attach wire btw spheres…what happens?What is final charge of each?
33Capacitance + - Units = Farads (F) Describes how much charge an arrangement of conductors can hold for a given voltage applied.-When the battery is connected to the pair of plates, charges will flow until the top plate’s potential is the same as the + side of the battery, and the bottom plate’s potential is the same as the – side of the battery. No potential difference.Q is the amount of charge on a plate and ΔV is the voltage applied to the platesUnits = Farads (F)
34Work to charge conductor Consider a spherical uncharged conductor, radius R. After a small amount of charge is placed on conductor, its potential becomes V = kQ/R (where V∞=0).To further charge conductor, work must be done to bring additional increments of charge, dQ, to place on surface. W = ΔV dQ…the amount of work increases as each dQ is added and sphere becomes more charged.
36Capacitance for Parallel Plates The E field is constantThe geometry is simple, only the area and plate separation are important.To calculate capacitance, we first need to determine the E-field between the plates. We did this using Gauss’ Law:separationdTotal charge qon inside of plateE and dAparallelarea AV+V-
37Need to find potential difference. Since E=constant Total charge qon inside of plateE and dAparallelV-V+area A
38How large is 1 Farad?If a parallel plate capacitor has plates that areseparated by only 1mm, in order to achieve 1F, the area of each plate would be…A = 1.1x108m2This corresponds to about 6 miles on each side of plate!Obviously, this is impractical to achieve large capacitance. Therefore, what do they do?
39Energy per unit VolumeIt is necessary at times to relate energy per unit volume to electric field of capacitor (parallel plate)
40ExampleCharge 8.0uF capacitor (C1) by connecting it to a 120V potential difference.Now remove the power supply.a) Find charge on capacitorb) Find energy stored in capacitor
41c) Now connect C1 to another capacitor, C2= 4.0uF, initially uncharged. What will be the potential difference across each capacitor & charge on each after equilibrium is reached?Conservation of charge
42Method for finding C for various geometries of plates 1) We are trying to calculate C where C = Q / ΔV2) In order to acquire ΔV, we must use3) Therefore we must find expression for E first using Gauss’ Law.4) Find E, then ΔV, and then C.
43Find capacitance of concentric cylindrical conductors with radius a (inside) & radius b. Inside charge is +, outside is -Field is radially outward
46Spherical Capacitor (2 concentric spheres, inner radius a & outer radius b as shown) +Q-Qba
47integrate inward instead of outward this time because of the negative we get with 1/r^2
48Combination of Capacitors & Equivalent Capacitance (CEQ) 1) Capacitors in Parallel & CEQ
49Consider 3 identical capacitors in parallel connected to battery of voltage, V. Find CEQ All top plates are at same potential and so are bottom plates, so…
50Splitting capacitor into 3 separate capacitors in parallel all with equal potential difference btwn them (same as battery)
51Capacitors in Series Charge on each capacitor is the same, Q. If you place 2 capacitors in series, the charge remains the same, but the potential difference is less for each capacitorCharge on each capacitor is the same, Q.
52Consider the individual voltages across each capacitor Since q is the same for eachThe sum of these voltages is the total voltage of the battery, V
53Combo Example Find Ceq, Q1, Q2, Q3, V1, V2, V3, & Qtotal A 12 battery is connected to the combination of capacitors as shown.8uFC1C2C312V2uF4uFFind Ceq, Q1, Q2, Q3, V1, V2, V3, & Qtotal
54DIELECTRICSEIf the strength of the electric field between the plates of an air filled capacitor becomes too strong, then the air can no longer insulate the charges from sparking (discharging) between the plates. For air, this breakdown occurs when the electric field is greater than 3x106 V/m. (this is what occurs during a lightning strike)…V/m is equivalent to N/C.In order to keep this from happening, an insulator, or dielectric, is often inserted between the plates to reduce the strength of the electric field, which yields a larger capacitance.
55Why does dielectric reduce E? Dielectric material is polar and molecules polarize as shown.The charge alignment creates an E-field within the material which OPPOSES the original E-field between the plates.Electrical forces create a torque to rotate and align molecules
56The dielectric is measured in terms of a dimensionless constant, κ (greek kappa) ≥ 1. (see table)
57Assuming a capacitor is charged with no power source present, dielectric reduces E which reduces V (according to V = Ed) while d remains constant. If V reduces, then C increases (according to C = Q / V)
58exampleA parallel-plate air capacitor is charged by placing a 90-V battery across it. The battery is then removed. An insulating, dielectric fluid is inserted between the plates. The voltage across the capacitor is now 28V. What is the dielectric constant of the fluid?
59Example 2A parallel-plate air capacitor holds a charge of 30nC when a voltage of V is placed across its plates. If the battery is not removed and a dielectric fluid is inserted between the plates, the charge on the plates increases to 87nC. Find the dielectric value.
60The charged plates of an air-filled capacitor are 10 cm by 20 cm and the gap between the plates is 6 mm. What is the capacitance when its gap is only half-filled with a dielectric having κ = 3.0?We treat this problem as 2 dielectrics in SERIES
61Dielectric application - computer key on keyboard When the key is pressed, the plate separation is decreased and the capacitance increases. Each key corresponds to a different capacitance.
62Dielectric application: Stud-finder (how you doin!)The dielectric constant of wood (and of all other insulating materials, for that matter) is greater than 1; therefore, the capacitance increases. This increase is sensed by the stud-finder's special circuitry, which causes an indicator on the device to light up.