PHY2049ch24A%281-27-10%29 - What You Already Know...

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Unformatted text preview: What You Already Know Coulomb’s law Electric fields Gauss’ law Electric fields for several configurations Point Line Plane (nonconducting) Sheet (conducting) Ring (along axis) Disk (along axis) Sphere, including (r) Cylinder, including (r) Dipole (along || and axes) PHY2049: Chapter 24 1 Chapter 24: Electric Potential Electric Potential Energy Electric Potential Equipotential Surfaces Potential of Point Charge Potential of Charge Distribution Calculating the Field from the Potential Potential Energy from a System of Charges Potential of Isolated Charged Conductors PHY2049: Chapter 24 2 Reading Quiz: Chapter 24 An equipotential surface is: a) b) c) d) e) a surface where the electric field is constant always parallel to the electric field a surface where the potential is zero always perpendicular to the electric field a surface where the electric field is zero PHY2049: Chapter 24 3 Reading Quiz: Chapter 24 The volt is a unit of: a) b) c) d) potential energy electric field potential force PHY2049: Chapter 24 4 Reading Quiz: Chapter 24 Electric potential is: a) a scalar quantity b) a vector quantity c) can be either scalar or vector PHY2049: Chapter 24 5 Work and Potential Energy From Physics 1 Find work moving object from to using constant force F W AB xB xA F dx = F xB x A ( ) A 1 2 3 B F = const is an example of a “conservative” force Work depends only on endpoints, not on path (e.g., 1, 2 or 3) Allows us to define “potential energy” U(x,y,z) W AB = F x B x A = U A U B Example: Work done by gravity for an object falling from a height h to height 0 ( ) W AB = mgh = U A U B U A = mgh U B = 0 6 PHY2049: Chapter 24 Conservation of Energy In general, if F is a conservative force, then: xB xA xB xA F dx = (U B UA KA ) Conservative force Work and kinetic energy Conservation of energy F dx = KB K A + U A = KB + U B Conservation of energy applies only when conservative forces are acting. Gravitational force is conservative So is electrostatic force, as we see now PHY2049: Chapter 24 7 Electric Work and Potential Energy Point charges Q, q: Work moving charge q from A B So Coulomb force is conservative (path independent) W AB kQq = rA kQq = UA UB rB PHY2049: Chapter 24 kQq Ur= r 8 () Electric Force is Conservative Holds in all electrostatic situations (not just point charge) Proof: integrate over any charge distribution Work done by electric field moving charge q from i to f Calculate from difference of potential energies i Charges q f Work: Welec = U fi = U i U f PHY2049: Chapter 24 9 Problem: Electric Potential Energy Two identical +12 mC point charges are initially spaced 5 cm from each other. If they are released at the same instant from rest, how fast will they be moving when they are very far from each other? Assume m1 = m2 = 1.0 g. PHY2049: Chapter 24 10 Gravitational & Electric Potential Energy Gravity A + + + + + + + A d Electric B h B Point B at lower potential energy than point A (q > 0) PHY2049: Chapter 24 11 Electric Potential Potential = PE per unit charge b Potential difference: constant E ------------------- Va Vb = E x b x a = Ed Potential difference: general E field ( ) d E +Q Va Vb = b a E ds Potential higher at + charges and “falls” to lower value at charges +q: Moves from higher to lower V q: Moves from lower to higher V PHY2049: Chapter 24 +++++++++++ 12 a Units for V and E Units of potential: “volt” V = U/q Volt = Joule / Coulomb Units of electric field F = Eq V = Ed E = F/q E = V/d Newton / Coulomb Volt / Meter So 1 V/m = 1 N/C Scientists and engineers prefer to use V/m PHY2049: Chapter 24 13 Potential of Point Charge Point charge q (using V = 0 at r = ) U kQ V= = q r Only true for point charge Example: Potential at surface of proton (r = 10-15 m) ke 9 10 1.6 10 V= = 15 r 10 ( 9 )( 19 ) = 1.44 106 = 1.44 MV PHY2049: Chapter 24 14 Energy Units: Electron Volts 1 eV = energy of charge e accelerated through 1 Volt We use energy units extensively in this course Let q = 4e and V = 2000 V K = 4 2000 = 8000eV = 8keV K = 8000 ( 1.6 10 19 ) = 1.28 10 15 J 15 PHY2049: Chapter 24 ConcepTest: Electric Energy A proton and an electron are each accelerated across a region of constant E field. Which has larger acceleration? (a) (b) (c) (d) proton electron both have equal acceleration neither one accelerates F = Ee a = F/m = Ee/m me mp Electron is much lighter than proton PHY2049: Chapter 24 16 ConcepTest: Electric Energy Which has the biggest increase in KE? (a) (b) (c) (d) proton electron both have the same increase in KE KE = 0 for both K = Fd = Eed Ve > Vp PHY2049: Chapter 24 17 Equipotential Surfaces Equipotentials: Contours of constant potential No work to move charge along contour: W = q V = 0 Equipotentials for point charge are shells (constant r) E equipotential surface Move a distance ds along the equipotential (dV = 0) Since dV = E ds = 0 path is always perpendicular to E See PHY2049: Chapter 24 18 Equipotential: Point Charge Equipotentials kQ V= r PHY2049: Chapter 24 19 Equipotential: Dipole PHY2049: Chapter 24 20 Equipotential: Constant E Field Constant E PHY2049: Chapter 24 Example: Capacitor 21 Topographic Map: Equal Altitude Contours Contour: Line of constant gravitational potential PHY2049: Chapter 24 22 ...
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