Capacitance Physics 102 Professor Lee Carkner Lecture 12

At which times do you have a final (select all that apply)? (These are the times for multi-section finals, don’t answer if you don’t have a final at any of these times.) A)Monday 6-8pm B)Tuesday 6-8 pm C)Wednesday 6-8 pm D)Wednesday 3-5 pm E)Thursday 3-5 pm F)I have a multi-section final, but I don’t know when

PAL #11 Potential  Find potential 1 meter and 5 meters away from -7.00nC charge  V = kQ/r  V 1 = (8.99X10 9 )(7X10 -9 )/1 = V  V 5 = (8.99X10 9 )(7X10 -9 )/5 = V  Change in potential energy between the two points   V = = V   PE = q  V = (1.6X )(50.34) = 8.05X J

PAL #11 Potential  What is energy and velocity at 1 meter?  Negative charge repels negative charge, so electron slows down  KE f = KE i -  PE  KE i = ½mv 2 = (0.5)(9.1X )(8.77X10 6 ) 2 = 3.50X J  KE f = 3.50X – 8.05X = 2.7X J  v = (2KE f /m) ½ = [(2)(2.7X )/(9.1X )] ½ = 7.7X10 6 m/s

PAL #11 Potential  (Optional part b) What is initial speed a long distance away?  For large distance away, V = 0   V = = V (between 5 meters and very far away)   PE = q  V = (1.6X )(12.95) = 2.07X J  Energy at gun is equal to the energy at 5 meters plus this  PE  KE f = 3.50X X = 3.71X J  v = [(2)(3.71X )/(9.1X )] ½ = 9.03X10 6 m/s

Equipotentials   Each line represents one value of V  Particles moving along an equipotential do not gain or lose energy  Equipotentials cannot cross  Blue = field = E Dashed = potential = V

Capacitance  A capacitor is a device that can store charge and thus energy   The amount of charge depends on the potential difference across the capacitor and the intrinsic properties of the device  This intrinsic property is called capacitance and is represented by C

Capacitance Defined  The amount of charge stored by a capacitor is just: Q = C  V  Or, defining the capacitance: C = Q/  V   The units of capacitance are farads (F) 1 F = 1 C/V   Typical capacitances are much less than a farad:  e.g. microfarad =  F = 1 X F

Capacitor Info  A capacitor generally consists of two parallel metal plates   Consider a battery connected across two metal plates   Electrons are attracted to the positive terminal and are lost by the second plate   Plates can’t touch or charge would move together and cancel out

Capacitor Diagram VV VVQ

Capacitor Properties  The capacitance depends on four things:   The distance between them (d)  The dielectric constant of the material between the plates (  )   The permittivity of free space (  0 )  A constant:  0 = 8.85 X C 2 /N m 2  C =  0 (A/d)

Dielectrics in Capacitors  The properties of the material between the plates is important   The polarized material partially cancels out the electric field between the plates

Dielectrics  The dielectric reduces the effective voltage   A dielectric allows a capacitor to store more charge with the same voltage   The dielectric also allows you to move the plates closer together without touching

Breakdown  The dielectric must be an insulator   If the voltage is large enough, the charge will jump across anyway   While Q = CV, there is a limit to how much we can increase Q by increasing V   Normally about 20 million volts

Energy in a Capacitor   Every little batch of charge increases the potential difference between the plates and increases the work to move the next batch   Charge stops moving when the  V across the plates is equal to the max  V possible for the circuit

Total Energy  Energy = 1/2 Q  V =1/2 C (  V) 2 = Q 2 /2C  since Q = C  V   At very large  V the capacitor will discharge by itself

Using Capacitors  Capacitors store energy  Generally only for short periods of time   Useful when you need a quick burst of energy   For a flash, capacitor is discharged into a gas (like xenon) that will glow when ionized  Since capacitance depends on d, can also use capacitance to measure separation 

Next Time  Exam #2  Bring calculator and pencil  For Monday January 12  Read ,  Homework Ch 18, P: 3, 4, 26, 27

PAL #13 Capacitors  C stored on capacitor at 1000 volts  What is capacitance?  Q= CV  C = Q/V = 0.005/1000 = 5X10 -6 F = 5  F  Jury-rig a replacement out of metal foil and Teflon coating (k = 2.1, thickness = 0.01 mm).  C =  0 A/d  A = Cd/  0 = (5X10 -6 )( )/(2.1)(8.85X )  A = 2.69 m 2  How can such a device be portable?  Roll it up, making sure the foil won’t short

Electric Potential Chart sign of  U sign of  V sign of Wnaturally? + charge moves with E field + charge moves against E field -charge moves with E field -charge moves against E field Yes No

When a charge +Q is placed at the corner of a square the potential at the center is 3 volts. What is the potential at the center if charges of +Q are placed on all corners of the square? A)0 V B)3 V C)9 V D)12 V E)24 V

If a positive charge moves with the field, A)PE increases, V decreases, Work positive B)PE increases, V decreases, Work negative C)PE increases, V increases, Work negative D)PE decreases, V increases, Work positive E)PE decreases, V decreases, Work positive

If a positive charge moves against the field, A)PE increases, V decreases, Work positive B)PE increases, V decreases, Work negative C)PE increases, V increases, Work negative D)PE decreases, V increases, Work positive E)PE decreases, V decreases, Work positive

If a negative charge moves with the field, A)PE increases, V decreases, Work positive B)PE increases, V decreases, Work negative C)PE increases, V increases, Work negative D)PE decreases, V increases, Work positive E)PE decreases, V decreases, Work positive

If a negative charge moves against the field, A)PE increases, V decreases, Work positive B)PE increases, V decreases, Work negative C)PE increases, V increases, Work negative D)PE decreases, V increases, Work positive E)PE decreases, V decreases, Work positive

If a charged particle moves along an equipotential line (assuming no other forces), A)Its potential energy does not change B)No work is done C)Its kinetic energy does not change D)Its velocity does not change E)All of the above