Capacitance, Dielectrics, Electric Energy Storage Chapter 22 Capacitance, Dielectrics, Electric Energy Storage

Capacitors & capacitance Capacitor / condenser: device that stores charge For a given capacitor: Q ∝ V Q R C: Capacitance of capacitor +Q - Q Unit: farad (F), μF & pF Symbol in diagram: 2

Capacitance depends on Capacitors Capacitance depends on Size, shape, relative position, insulating material 3

Determine capacitance For a parallel-plate capacitor: +Q - Q S d (ignoring edge effect) 4

Cylindrical capacitor Example1: A capacitor consists of two coaxial cylindrical shells (R1, R2), both with length L>>R2. Calculate the capacitance. L R1 R2 5

Spherical capacitor Question: A capacitor consists of a sphere surrounded by a concentric spherical shell (R1, R2). Calculate the capacitance. Q2 Q1 R1 R2 - Q1 Q1+Q2 6

Capacitors in series and parallel 2) In parallel 7

Capacitor combination Example2: Are the capacitors in series or parallel? 1) 2) parallel parallel Example3: How does C, Q, V change if d → 2d ? d 8

Electric energy storage Charged capacitor stores electric energy Work required to store charges: +q - q dq Energy stored: 9

Electric energy is stored in the electric field! Energy in the field How does the electric energy distribute? d S Energy per unit volume / energy density: Electric energy is stored in the electric field! 10

Energy in capacitor Example4: A parallel-plate capacitor is charged at 220V. (a) What is the capacitance; (b) how much electric energy can be stored? d = 1mm S =10cm2 Solution: (a) (b) Energy stored: Maximum U ? 11

Solution: 2 methods to solve it. Different methods Example5: Determine the electric energy stored in a spherical capacitor. Q R1 R2 - Q Solution: 2 methods to solve it. a) By using the capacitance: Energy stored: 12

b) By using the energy density: Q R1 R2 - Q Total energy: Q Discussion: Isolated conductor sphere? 13

Insulating material in capacitors → dielectric Dielectrics Insulating material in capacitors → dielectric ① Harder to break down → V ↗ ② Distance between plates ↘ ③ Increases the capacitance: where K is the dielectric constant Also noted as : relative permittivity 14

Permittivity of material If a dielectric is completely filled the space: : the permittivity of material In a specific region filled with dielectric: All in electric expressions → 15

Electrostatics in dielectric In a specific region filled with dielectric: field is reduced but not zero The energy density in a dielectric: Example6: How does C, Q, U change? C V battery disconnected? 16

Half filled dielectric Question: How does the capacitance change if the capacitor is half filled with dielectric? (S, d, K) 1) 2) 17

Molecular description (1) There are two different types of dielectrics: 1) Polar dielectrics, such as H2O and CO Have permanent electric dipole moments. - + 2) Nonpolar dielectrics, such as O2 and N2 No permanent electric dipole moments. 18

Molecular description (2) Polar Nonpolar Q -Q Polarization - + Induced field Eind Bound charge 19

Thinking & question Thinking: Why charged objects can attract small paper scraps or water flow? C V Question: Move a dielectric plate out of a charged capacitor, the electric energy increases, where does the extra energy come from? 20

Brief review of Chapter 19-22 Coulomb’s law: Gauss’s law: Electric potential: Capacitance; Electric energy: Dielectrics: 21

These chapters should be studied by yourself Some useful concepts and equations: Ohm’s law: V = I R Current & resistance Current density: Microscopic statement of Ohm’s law: (ch23, pr.24) conductivity & resistivity 22