February 6. Physics 272. Spring Prof. Philip von Doetinchem

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1 Physics 272 February 6 Spring Prof. Philip von Doetinchem philipvd@hawaii.edu Phys272 - Spring 14 - von Doetinchem - 216

2 Summary Charges on all plates have the same magnitude Equivalent capacitance of a series combination of capacitors is always less than any individual capacitance. Phys272 - Spring 14 - von Doetinchem - 217

3 Summary Charges can reach capacitors independently from the source Imagine one big capacitor that you split into multiple smaller capacitors The parallel combination of capacitors always has a higher capacitance than the individual capacitances Charges are generally not the same on each capacitor Phys272 - Spring 14 - von Doetinchem - 218

of capacitors always has a higher capacitance than the individual capacitances

4 Energy storage in capacitors and electric-field energy Many important applications of capacitors rely on storing energy Electric potential energy stored in a charged capacitor is equal to the amount of work to separate opposite charges Discharging of capacitor: electric field between does work Phys272 - Spring 14 - von Doetinchem - 219

capacitor is equal to the amount of work to separate opposite charges Discharging of

5 Energy storage in capacitors and electric-field energy Potential energy of uncharged capacitor set to zero Capacitance measures the ability to store energy and charge Charging of capacitor: charge increases and energy increases Less work is required to transfer charge if capacitance is higher Phys272 - Spring 14 - von Doetinchem - 220

and charge Charging of capacitor: charge increases and energy increases Less work

6 Applications of capacitors: energy storage Electronic flash units in cameras Capacitor is discharged when shutter button is pressed Charge goes to flash tube Capacitor can smooth out unwanted variations in voltage surges more in ~2 weeks Phys272 - Spring 14 - von Doetinchem - 221

goes to flash tube Capacitor can smooth out unwanted variations in

7 Z machine Phys272 - Spring 14 - von Doetinchem - 222

8 Electric field energy Charge a capacitor by moving electrons from one plate to the other: work against the electric field between the plates Energy is stored in the field in the region between the plates Energy per unit volume (energy density): Phys272 - Spring 14 - von Doetinchem - 223

Energy is stored in the field in the region between the plates Energy

9 Electric field energy Not only valid for parallel-plate capacitors true for any electric field configuration in vacuum Vacuum can have electric fields and is in this sense not really empty Two interpretations: energy is property of an electric field or a shared property of all charges creating the field Phys272 - Spring 14 - von Doetinchem - 224

sense not really empty Two interpretations: energy is property of an electric field or

10 Eletric field energy Magnitude of electric field to store 1J in a volume of 1m3 Relation between electric field and energy density Dry air can sustain ~3MV/m without breaking down Phys272 - Spring 14 - von Doetinchem - 225

field and energy density Dry air can sustain ~3MV/m

11 Energy stored in a capacitor Phys272 - Spring 14 - von Doetinchem - 226

12 Energy stored in a capacitor Phys272 - Spring 14 - von Doetinchem - 227

13 Dielectrics Most capacitors have non-conducting material between them: dielectric Helps separating two oppositely charged conductors Prevents ionization of the air and allows for higher potential build up before discharges occur store higher energies Phys272 - Spring 14 - von Doetinchem - 228

ionization of the air and allows for higher potential build up before

14 Dielectrics Phys272 - Spring 14 - von Doetinchem - 229

15 Dielectrics constant voltage: separation between plates widened: plates closer together: electrometer shows charge flowing off of the plates electroscope shows no change in voltage charge flows back onto of the plates fixed amount of charge onto left plate: separation is widened Plexiglass inserted between the plates: electroscope shows a rising voltage (charge stays constant) voltage drops When plexi is removed voltage rises back up again charge is still there Phys272 - Spring 14 - von Doetinchem - 230

plate: separation is widened Plexiglass inserted between the plates: electroscope shows a rising voltage (charge stays

16 Dielectrics Charge stays constant Insert dielectric: voltage drops C=Q/V capacitance increases with dielectric Dielectric constant: K=Cdielectric/Cvacuum For a given charge the potential difference is reduced by a factor K K is always larger than unity Air has K= Water has K=80.4 poor conductor, but good solvent ions dissolve in water current flow Dielectrics always show some leakage (no perfect insulators) Phys272 - Spring 14 - von Doetinchem - 231

is always larger than unity Air has K=1.0006 Water has K=80.

17 Induced charge and polarization When dielectric is inserted and charge is kept constant potential difference drops electric field drops surface charge density drops, but not the charge Redistribution of charges in dielectric occurs: polarization Phys272 - Spring 14 - von Doetinchem - 232

surface charge density drops, but not the charge Redistribution of

18 Induced charge and polarization Phys272 - Spring 14 - von Doetinchem - 233

19 Induced charge and polarization High capacitances can be reached with a dielectric with high K value Phys272 - Spring 14 - von Doetinchem - 234

20 Capacitor with and without dielectric Phys272 - Spring 14 - von Doetinchem - 235

21 Capacitor with and without dielectric 0 Phys272 - Spring 14 - von Doetinchem - 237

22 Capacitor with and without dielectric Field does work on dielectric to polarize Phys272 - Spring 14 - von Doetinchem - 238

23 Moving dielectric into capacitor Phys272 - Spring 14 - von Doetinchem - 239

24 Moving dielectric into capacitor Phys272 - Spring 14 - von Doetinchem - 240

25 Moving dielectric into capacitor Phys272 - Spring 14 - von Doetinchem - 241

26 Moving dielectric into capacitor Phys272 - Spring 14 - von Doetinchem - 242

27 Dielectric breakdown Dielectric can become a conductor Electrons are ripped loose from atoms creates an avalanche arcing or lightning Discharge can cause damage to capacitors and circuits conducting path allows charge to flow where it is normally not allowed Depends on temperature and pressure, purity of material Phys272 - Spring 14 - von Doetinchem - 245

28 Molecular model of induced charge Dielectric has no free charges where is the induced charge coming from? If material molecules have an electric dipole moment alignment of dipoles in electric fields If no dipoles in dielectric: electric field induces dipoles dipoles align in field Phys272 - Spring 14 - von Doetinchem - 246

29 Gauß's law in dielectrics Calculation only requires knowledge of K of dielectric and the free charge on the conductor Phys272 - Spring 14 - von Doetinchem - 247

30 Review Any pair of insulated conductors forms a capacitor A charged capacitor has charges of the same amount and opposite sign on the insulated conducting sides Capacitance is a property that defines how much charge can build up at a certain voltage and is determined by the dimensions Circuits with capacitors in parallel have a higher equivalent capacitance than the individual capacitors Circuits with capacitors in series have a lower equivalent capacitance than the individual capacitors Energy can be stored in the electric field between the conductors Dielectrics between the conductors of a capacitor change the capacitance and can be used to build elements with high capacitance Phys272 - Spring 14 - von Doetinchem - 248

31 Discussion Suppose the two plates of a capacitor have different areas. When the capacitor is charged by connecting it to a battery, do the charges on the two plates have different or equal magnitude? The freshness of fish can be determined by placing a fish between plates of a capacitor and measuring the capacitance. Why? Due to the attraction of the opposite charges on the plates, charge will be on only that part of the larger plate that is directly across from the smaller plate. Both the capacitor and the battery remain neutral; the two plates have charges of equal magnitude. The capacitance depends on the dielectric constant of the fish and this in turn depends on the amount of water in the fish s tissue. Liquid dielectrics that have polar molecules always have dielectric constants that decrease with increasing temperature. Why? Increasing temperature increases the kinetic energy of the molecules and this decreases the alignment of their molecular dipoles. This decreases the electric field they produce that opposes the electric field due to the charges on the plates. Phys272 - Spring 14 - von Doetinchem - 249

Q24.1 The two conductors a and b are insulated from each other, forming a capacitor. You increase the charge on a to +2Q and increase the charge on b

Q24.1 The two conductors a and b are insulated from each other, forming a capacitor. You increase the charge on a to +2Q and increase the charge on b to 2Q, while keeping the conductors in the same positions.