Chapter 26:Capacitance and Dielectrics

Capacitors A capacitor is made up of 2 conductors carrying charges of equal magnitude and opposite sign. The Capacitance (C) of a capacitor is defined as: where Q is the charge on either conductor and ∆V is the potential difference between them The SI unit of conductance is the farad (F). -  1 F = 1 coulomb per volt (C/V)

Parallel-Plate Capacitors Two metallic plates of equal area “A” are separated by a distance “d”. One plate carries a + charge while the other carries a – charge. The surface density of each plate is The electric field between the plates is

Parallel-Plate Capacitors Since the field between the plates is uniform and points directly from one plate to the other, the magnitude of the potential difference between the two equals Ed Therefore the capacitance is given by:

Combinations of Capacitors Capacitors can be combined in electric circuits. When studying circuits a circuit diagram can be used and specific circuit symbols are given to designate a capacitor, battery, and switch. Capacitor Symbol Battery SymbolSwitch Symbol

Various Combinations Parallel Combination ∆V1=∆V2=∆V Q total=Q1+Q2 Equivalent capacitor Q total = C equiv (∆V) C equiv = C1+C2+C3… Series Combination ∆V total =∆V1+∆V2 Q1=Q2=Q Equivalent capacitance 1/C equiv = 1/C1 + 1/C2 + 1/C3…

Energy Stored in Charged Capacitor Electric potential energy is stored in the system Energy stored in a charged capacitor The energy in a capacitor is stored in the electric field between the two plates as the capacitor is charged. The electric field is proportional to the charge on the capacitor

Capacitors with Dielectrics A Dielectric is a non-conducting material like rubber or glass. The Dielectric constant (κ) varies from from one material to the next. The capacitance of a capacitor containing a dielectric is: With the addition of the dielectric the charge remains the same, the potential difference decreases, and the capacitance increases. The capacitance increases by the factor “κ” when the dielectric is filling the space between the plates.

Electric Dipole in an Electric Field The Electric dipole moment has a magnitude of p=2aq 2a is the distance between – q and + The torque on an electric dipole in a uniform electric field is given by: The potential energy of the system of an electric dipole in a unifrom external electric field is given by:

Atomic Description of Dielectrics The field in the presence of a dielectric equals Charged dipoles can be viewed as creating another pair of parallel plates establishing an electric field So, the net electric field in the dielectric has a magnitude