Chapter 17 Electric Potential and Electric Energy; Capacitance

Electric Potential and Electric Energy; Capacitance Review of Chapter Electric Potential and Potential Difference 17.2 Relationship between Electric Potential and Electric Field 17.3 Equipotential Lines 17.4 The Electron Volt, a Unit of Energy 17-5 Electric Potential Due to Point Charges 17-6 Electric Dipoles 17-7 Capacitance 17-8 Dielectrics 17-9 Storage of Electric Charge Cathode Ray Tube The Electrocardiogram

Important stuff from Chapter 16: Coulomb’s Law: F = kQ 1 Q 2 /r 2 where: k = 9.0 x 10 9 Nm 2 /C 2 Q 1 & Q 2 are two charges (coulomb) r = distance between two charges

Important stuff from Chapter 16: Electric Field (E)—force (F) exerted on a positive test charge divided by the magnitude of the charge (q, coulombs) E = F/q (units N/C)  electric field goes from positive to negative (the path of a positive test charge)

Important stuff from Chapter 16: Electric Field due to a Point Charge: E = kQ/r 2

Important stuff from Chapter 16: Electric potential energy—the energy stored in a charged objects when its in an electric field positive when the two charges are the same (repulsive) and negative when the two charges are opposite (attractive)

Electric Potential and Potential Difference To move an charge in an electric field work must be done.

Electric Potential and Potential Difference  change in electric potential energy (PE a – PE b ) when a charge, q, moves from point b to point a is the negative work done by the electric force to move the charge from b to a  PE of a charge is the largest when it is closest to the plate with the same charge ba

Electric Potential and Potential Difference Electric Potential (potential)— the potential energy per unit charge (V) V a = PE a /q --for a test charge, q, at point a in an electric field Where is the test charge’s electric potential the most, at point a or b? Positive plate has higher potential than negative (by definition, why?) ba

Electric Potential and Potential Difference Can only measure differences in PE; so can measure the potential difference (difference in potential) between two points Since potential difference (PE a – PE b ) =  W then V ab = V a  V b =  W ba /q ba

Electric Potential and Potential Difference V ab = V a  V b =  W ba /q Unit; volt (1 V = 1 J/C) Voltage = potential difference Zero for voltage is arbitrary since we can only measure  PE ba

Electric Potential and Potential Difference Since electric potential (V) = PE/q then  PE = PE b  PE a = qV ba if an object with charge q moves through a potential difference V ba its potential energy changes by an amount qV ba electric potential difference is a measure of how much energy an electric charge can acquire in a situation and also a measure of how much work a charge can do ba

Electric Potential and Potential Difference Accelerating a charge;  PE = qV =  KE so v =  (2qV/m) since KE = ½ mv ba

Relationship between Electric Potential and Electric Field In a uniform electric field (parallel plates) to move a charge: W = qV = Fd = qEd (since F = Eq) so V = Ed or E (electric field) = V/d

Equipotential Lines Equipotential lines—graphic representation of electric potential Potential the same on lines so it takes no work to move charges along the lines Always perpendicular to field lines (diagram p.507) Continuous lines, never end A conductor must be entirely at the same potential in the static case or electrons would accumulate at its surface

Equipotential Lines Equipotential lines— graphic representation of electric potential Always perpendicular to field lines (diagram p.507)

The Electron Volt; Unit of Energy Electron Volt (eV)—used to measure very small energies (electrons, atoms, molecules, etc.) Energy acquired by a particle carrying the charge of one electron as a result of moving through a potential difference of 1 volt 1 eV = 1.6 x 10  19 J (q e =  1.6 x 10  19 C) electrons accelerated through potential difference of 10V loses 10V of PE and gains 10V of KE

Electric Potential due to Point Charges V = kQ/r where Q = point charge, r = distance between point and test charge and k = ? V represents the absolute potential since the V at r =  equals zero So V  Q and V  1/r but E  1/r 2 (remember E = kQ/r 2 )

Electric Dipoles electric dipole--two equal point charges (Q) of opposite sign separated by a distance dipole moment--the product of charge times length (Ql) polar molecules—molecules that have a dipole moment

Capacitance capacitor—a device that can store electric charge consists of two conducting objects placed near each other but not touching widely used in electronic: camera flash, surge protectors, energy backups, memory for binary code (RAM) often consists of two parallel plates (of area A, and separation d) rolled together with an insulating material between them symbol : —||—

Capacitance Capacitors Leydon Jar

Capacitance capacitor—a device that can store electric charge (diagram)

Capacitance Amount of charge acquired by a given capacitor Q = CV where: Q = amt. of charge (C) V = potential difference (V) C = capacitance of capacitor (constant of proportionality dependent on properties of capacitor)-- units farad (F) = Coulombs/Volts

Capacitance For a parallel plate capacitor: C =  o A/d where:  o = permittivity of free space = 8.85 x 10  12 C 2 /Nm 2 (remember)

Dielectrics Dielectric—the insulating sheet between the plates of a capacitor Serves several purposes: Allows higher voltages to be applied without charge passing the gap, dielectrics break down less readily than air Allows plates to be closer together, the closer the plates are the larger the capacitance of the capacitor (WHY?)

Dielectrics For a parallel plate capacitor: C = K  o A/d where: K = dielectric constant (Table 17-3) Since C =  o A/d then  = K  o where:  = the permittivity of the material

Dielectrics Molecular Description of dielectrics With air between plates; only plates of capacitor have a potential difference

Dielectrics Molecular Description of dielectrics With a dielectric; molecules of dielectric can line up in electric field of capacitor plates causing a net negative side by positive plate and a net positive by negative plate (even though charges do not move in dielectric material— insulator)

Dielectrics Molecular Description of dielectrics A positive test charge within the dielectric does not feel the full force of the electric field of the capacitor so it takes a greater potential difference between the two plates of the capacitor to cause it to move in the dielectric

Storage of Electric Energy A charged capacitor stores electric energy The net effect of charging a capacitor is to remove charge from one plate and add it to another (using a source of electricity—battery)

Storage of Electric Energy A capacitor is not charged instantly—it requires time and work to do this and this increases with increasing charge on plates (?) If the work were constant then the work required to charge a capacitor would be W = QV But since it is not we deal with the average voltage (1/2 of V f + V I ) so W = Q V f /2 (why?)

Storage of Electric Energy Internal energy stored in a capacitor is: U = 1/2QV where: V is potential difference between plates Since Q = CV then: U = ½ Q 2 /C and since C =  o A/d & V = Ed then U = 1/2  o E 2 A/d

Storage of Electric Energy Energy density (u)—energy per unit volume u = energy/volume = 1/2  o E 2

Cathode Ray Tube Read section and know this: What is a CRT? What is thermionic emission? What is a cathode? What is an anode? Explain how a cathode ray tube works. What is an oscilloscope? Explain how an electrocardiogram measures heart function. Extra Credit: Find out about LCD, LED and Plasma screens (for TV’s)

Cathode Ray Tube Explain how a cathode ray tube works.

Cathode Ray Tube What is an oscilloscope?

The Electrocardiogram Explain how an electrocardiogram measures heart function.