Capacitors Q D A capacitor is a device that is capable of storing electric charges and thus electric potential energy. => charging Its purpose is to release them later in a controlled way. => discharging Capacitors are used in vast majority of electrical and electronic devices. +Q -Q Typically made of two conductors and, when charged, each holds equal and opposite charges.

Polar and Nonpolar Dielectrics Polar dielectrics: dielectric material whose molecules have permanent electric dipole moments, such as water. Eext = 0: the orientations of the permanent electric dipoles are distributed randomly, so the net dipole moment of the material is zero. Eext  0 : the molecular dipoles try to align themselves with the field against random thermal motion, resulting in a net dipole moment. Nonpolar dielectrics: molecules with no permanent electric dipole moments. Eext  0 :  charges separate, induced dipole moment emerges. Show the first demo:5A-31

Dielectrics between Capacitor Plates + Q - Q free charges Electric field E between plates can be calculated from Q – q. neutral -q +q The presence of a dielectric weakens the electric field, therefore weaken the potential drop between the plates, and leads to a large capacitance.

Inserting Dielectrics (= Insulator) Inserting a dielectric between the plates of a capacitor increases capacitance Q=CV holds more charges at fixed V Dielectric constant  of a dielectric is the ratio of the capacitance when filled with it to that without it:  > 1 always (dimensionless) Material  air (1 atm) 1.00059 paper 3.7 pyrex 5.6 water (20C) 80.4 strontium titanate 310 Under the same Q, V = V0/k E = E0/k Show demo: 5A-30. Dielectric strength: breakdown field per unit length Breakdown potential determined by dielectric strength (Emax)

Capacitors in Parallel  V is common Equivalent Capacitor: where

Capacitors in Series q is common Equivalent Capacitor: where 

Conductor inserted between plates A parallel-plate capacitor with conductor inserted in the middle Two capacitors of area A in series -Q a b +q -q +q a b a -q +q -q E=0 outside capacitors E=0 in conductor between plates between plates (a)

Warm-up quiz All the capacitors have the same capacitance C, What is the total capacitance? A). 4/3 C B). 3/4 C C). 3/2 C D). 1/2 C E). 2/3

Non-uniform Parallel-plate Capacitor 1 Equivalent to 2 capacitors in parallel Potential drop V in each is the same. Note if even though a

Non-uniform Parallel-plate Capacitor 2 Equivalent to 2 capacitors in series (Free) charge in each Q is the same. Note if +Q -Q +Q addition of the “animated” metal plate has no effect on the field in 1/4d and 3/4d since the field produced by +Q and –Q are cancelled -Q

Inserting Dielectric Material with Battery Disconnected Charge a parallel plate capacitor filled with air (or vacuum) to potential difference V0. Deposits charge Q 2. Disconnect the battery Q remains fixed -Q 3. Insert a dielectric of dielectric constant  Q So, V and E decreases from V0 , E0 to and -Q and

Inserting Dielectric Material with Battery Connected Charge a parallel plate capacitor filled with vacuum (air) to potential difference V. Deposits charge 2. Keep the battery connected V remains fixed 3. Insert a dielectric of dielectric constant  So, Q increases from Q0 and E remains fixed and and

Force between the plates of a capacitor What is the force between these charged plates? +Q -Q Battery disconnected Is it attractive? Yes! Is it ? Not quite! Force F acting on a charge q in the electric field E created by other source charges is given by: E created by the charge on the upper plate at the location of the lower plate is

Energy stored in a capacitor revisited +Q -Q Battery disconnected separation  0 +Q -Q separation  d External work required to separate the plates from zero to d m apart is When d = 0, Volume=0, i.e. U = 0 This is also the potential energy stored in capacitor. What if a battery remains connected?

Force and energy with battery connected, a mystery? Force between plates? +Q -Q Battery connected V attractive Work to change separation from 0 to d?  separation  0 +Q -Q Q changes separation  d separation d+d separation  d However,

Lecture quiz A. Five identical capacitors have the same capacitance C. Then capacitor (e) is filled with a material with dielectric constant k. What is the total capacitance? a b e c d A). 2C B). 1/(1+k) C C). (1+k)C D). 5 C E). [4/(4+k)] C

Lecture quiz B. Five identical capacitors have the same capacitance C. Then capacitor (e) is filled with a material with dielectric constant k. What is the total capacitance? a b e c d A). 2C B). [k/(1+k)] C C). (1+k)C D). [1/(1+k)] C C E). (4+k) C

Lecture quiz C. Four identical capacitors have the same capacitance C. Then capacitor (a) is filled with a material with dielectric constant k. What is the total capacitance? a b c d A). (3/2 + k) C B). (3+k) C C). 5/2 C D). (2/3 +k) C E). (3+k) C