(21/703) At what distance from a point charge of 8µC would the potential equal 3.6X10 4 V?

Transcription

1 (/73) At what distance from a point charge of 8µC would the potential equal 3.6X 4 V?

2 (6/73) A positron has the same charge as a proton but the same mass as an electron. Suppose a positron moves 5. cm in the direction of a uniform 48 V/m electric field. a) How much potential energy does it gain or lose? b) How much kinetic energy does it gain or lose?

3 (3/74) The Bohr model of the hydrogen atom states that the electron can only exist in certain allowed orbits. The radius of each Bohr orbit is given by the expression r=n (.59 nm) where n=,, 3, etc. Calculate the potential energy of a hydrogen atom when the electron is in the a) first allowed orbit n= b) the second allowed orbit n= c) when the electron has escaped from the atom, r=infinity. Express your answers in electron volts (ev=.6x -9 )

4 Capacitors

5 Capacitors are used to tune the frequency of radio receivers as filters in power supplies to eliminate sparking in automobile ignition systems as energy storage devices say for electronic flash units

6 A capacitor basically consists of two conductors separated by an insulator The capacitance of a given device depends on Its geometry The material separating the charged conductors the dielectric A dielectric is an insulating material having distinctive electrical properties The capacitance, C, of a capacitor is defined as the ratio of the magnitude of the charge on either conductor to the magnitude of the potential difference between them C = Q/V By definition capacitance is always a positive quantity The unit of capacitance is the Farad (F) [capacitance] = F = C/V Note: the farad is a large unit of capacitance and typical devices have capacitances on the order of micro- to pico-farads On a practical note capacitors are often labeled mf for microfarads and mmf for micro-microfarads = picofarads

7 Capacitance In general, the potential of an isolated conductor is proportional to the charge of the conductor. V Q For example, a spherical conductor: V=kQ/ The proportionality between V and Q is a constant that depends only on the shape of the conductor. Q V = constant We call this constant the capacitance of the conductor. It describes the capacity of the conductor to hold charge or a measure of the ability to store charge and electrical potential energy. The unit of capacitance: Farad = Coulomb/Volt.

8 Important: Capacitance only depends on geometry!!! For a given conductor, the ratio C=Q/V is a constant. It does not depend on charge or voltage in some independent way. If you change the geometry of a conductor, then the capacitance will change. But for a given geometry, the capacitance is a constant, and the charge and voltage always must change together. Take the example of the charged conducting sphere: V=kQ/. If you double the charge, the voltage must double too, and the ratio C=Q/V=/k will remain unchanged.

9 Capacitors Two conductors, carrying equal and opposite charges, form a device called a capacitor. r E +Q Q V In this case, we concern ourselves with the potential difference between the two conductors, not the potential with respect to infinity. The ratio, Q/V, is still a constant depending only on the geometry of the two conductors, and we call that ratio the capacitance of the capacitor.

10 Parallel Plate Capacitors V Two parallel conducting plates of area A are separated by a small distance d. d << A Each plate carries a surface charge density σ=q/a. The electric field between the plates is then E=σ/ε. A d r E The potential difference between the plates is then just V=Ed. V=Ed=σd/ε = Qd/Aε So, the capacitance is C=ε A/d.

11 Cylindrical Capacitors (I) Two concentric conducting cylinders of length L and radii and. We determine the electric field between the cylinders using Gauss s Law: we imagine a cylinder in between the other two. The enclosed charge is Q, and the < << L field is radial: E(πrL)=Q/ε r E = V C = πlε = V Q V V Q r rˆ where V is the magnitude of = πlε = ln( ) r r E dr = Q Q dr = ln( πlε r πlε the potential difference...a ) positive quantity

12 Cylindrical Capacitors (II) If ( )<< L, then the cylindrical capacitor acts much like a parallel plate capacitor. We revisit our integral for the potential difference. narrow, so we approximate the integral by taking dr V C = V V This has the form of and plate area = πlε A = r r E dr = πl (the area of Q Q dr πlε r πlε The interval from the curved surface of a cylinder). ( + ) is very / the capacitance of a parallel plate capacitor with spacing d = and r to.