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Questions 821 (26.10) These two equations enable you to simplify many electric circuits by replacing multiple Energy is stored in a capacitor because the charging process is equivalent to the transfer of charges from one conductor at a lower electric potential to another conduc- (26.11) When a dielectric material is inserted between the plates of a capacitor, the capaci- tance increases by a dimensionless factor 1, called the dielectric constant: (26.14) where C 0 is the capacitance in the absence of the dielectric. The increase in capaci- tance is due to a decrease in the magnitude of the electric field in the presence of the E arises from an internal electric field produced by aligned dipoles in the dielectric. The electric dipole moment p of an electric dipole has a magnitude (26.16) The direction of the electric dipole moment vector is from the negative charge toward The torque acting on an electric dipole in a uniform electric field E is (26.18) The potential energy of the system of an electric dipole in a uniform external electric field E is (26.20) U # $ p & E $ " p % E p ! 2aq C # 1C
0 U # Q 2 2C # 1 2 Q ∆V # 1 2 C( ∆V
) 2 1 C
eq # 1 C 1 & 1 C 2 & 1 C 3 & + + + Geometry Capacitance Equation Isolated sphere of radius R 26.2 (second spherical conductor assumed to have infinite radius) Parallel-plate capacitor of plate 26.3 area A and plate separation d Cylindrical capacitor of length 26.4 ! and inner and outer radii a and b, respectively Spherical capacitor with inner 26.6 and outer radii a and b, respectively C # 4 () 0 R C # ab k
e (b $ a) C # ! 2k
e
ln(b/a) C # )
0
A d Capacitance and Geometry Table 26.2 1. The plates of a capacitor are connected to a battery. What happens to the charge on the plates if the connecting 2. A farad is a very large unit of capacitance. Calculate the length of one side of a square, air-filled capacitor that has 3. A pair of capacitors are connected in parallel while an identical pair are connected in series. Which pair would be Q U E S T I O N S |