Tài liệu Chapter IX Conductors, Capacitors ppt

2/20/2008 1 GENERAL PHYSICS II Electromagnetism & Thermal Physics 2/20/2008 2 Chapter IX Conductors, Capacitors §1. Charges and electric field on conductors §2. Capacitance of conductors and capacitors §3. Energy storage in capacitors and electric field energy §4. Electric current, resistance and electromotive force 2/20/2008 3 §1. Charges and electric field on conductors: 1.1 The balance of charges on conductors: In conductors there are charged particles which can be freely move under any small force. Therefore the balance of charges on conductors can be observed under these circumstances:  The electric field equals zero everywhere inside the conductor E = 0 The electric potential is constant inside the conductor V = const  The electric field vector on the surface of conductors direct along the normal of the surface at each point E = En The surface of conductors is equipotential  Inside conductors there is no charge. This conclusion can be proved by applying the Gauss’s law for any arbitrary closed surface inside conductor. All the charge is distributed on the surface of conductors. 2/20/2008 4  Since the distribution of charge on conductors does not depend on the distribution of the matter the distribution of charges is the same for hollow and solid conductors.  The fact that the distribution of charges only on the surface of conductors can be understood as follows: Suppose that we provide the conductor with an amount of charges charges repulse mutually and tend to leave as far as possible each from other. 2/20/2008 5 1.2 The electric field at the surface of a conductor: Consider the red small cylindrical surface with the base dS. Applying the Gauss’s law for this closed surface we have The electric field in vacuum near the surface The electric field in dielectric environment near the surface (σis the surface charge density at the considered point on the surface) σ + Near convexes of the surface: the equipotential surfaces are dense E is large the charge density is large + Near deepenings of the surface: the equipotential surfaces are rare E is smaller the charge density is small 2/20/2008 6 §2. Capacitance of conductors and capacitors: 2.1 Charging by induction: A charge body (rod) can give another body a charge of opposite sign, without losing any of its own charge. Pictures: a) Metal sphere is initially uncharged b) Charged rod brought nearby c) Wire allows piled-up electrons to flow to ground d) Wire is disconnected from sphere e) Charged rod is removed: Electrons on sphere rearrange themselves. Metal sphere Isulating stand Negatively charged rod a) b) c) d) e) wire 2/20/2008 7 2.2 Capacitors and capacitance:  A capacitor is a device whose purpose is to store electrical energy which can then be released in a controlled manner during a short period of time.  A capacitor consists of 2 spatially separated conductors which can be charged to +Q and -Q respectively.  Definition: The capacitance of the capacitor is the ratio of the charge on one conductor of the capacitor to the potential difference between the conductors: V Q C  • The capacitance belongs only to the capacitor, independent of the charge and voltage. [The unit of capacitance is the Farad: 1 F = 1C/V] 2/20/2008 8 Example 1: Parallel Plate Capacitor • Calculate the capacitance. We assume +  , -  charge densities on each plate with potential difference V : d A - - - - - + + + + V Q C   Need Q:  Need V: from definition:  Use Gauss’ Law to find E (in next slide) 2/20/2008 9 Recall the formula for the electric field of two infinite sheets: • Field outside the sheets is zero Gaussian surface encloses zero net charge E=0 E=0 E  + + + + + + +  + + + - - - - - - - - - - + + - - - A A AQ   inside AESdE    • Field inside sheets is not zero: • Gaussian surface encloses non-zero net charge 0   E (Note that here we consider a capacitor in vacuum) 2/20/2008 10 00   A Q E  d A Q EdldEVV b a ab 0       d A V Q C 0   Remark: • The capacitance of this capacitor depends only on its shape and size • This formula is true for parallel-plate capacitor (shape), and C depends on A, d (size) (for another shape one has other formula). • When the space between the metal plates is filled with a dielectric material, the capacitance increases by a factor k (see the previous chapter) (Recall: k - dielectric constant; ε- permitivity of the dielectric) In order to increase C d (limitatively), and one must increase A, ε. [...]... b a 12 2.3 Capacitors in Parallel: a a VC 1 Q1 -Q1 Q2 -Q2 C 2 b  Q V C -Q b • Find “equivalent” capacitance C in the sense that no measurement at a, b could distinguish the above two situations • The voltage across the two is the same… Parallel Combination: Equivalent Capacitor: 2/20/2008  C Q1 Q 2 Q 2 Q1 2 V   C1 C1 C 2 Q Q Q Q (C  ) C C  1 2  1 1 2 V V C1V  C12 C C 13 2.4 Capacitors. .. on the inner plates of C1 and C2 assume there is no net charge on node between C1 and C2 Q  C RHS: LHS: 2/20/2008 V ab Q Q Vab  1  2   V V C1 C2  1 1 1   C C1 C 2 14 Examples: Combinations of Capacitors a  C3 b C 1 a C 2 b C • How do we start?? • Recognize C3 is in series with the parallel combination on C1 and C 2 i.e., 1 1 1   C C3 C1  2 C 2/20/2008  C 3 ( C1  2 ) C C C1  2  3 C...   C  • The total work W to charge to Q is then given by: Q 1 1 Q2 W    qdq C0 2 C • In terms of the voltage V: 2/20/2008 Look at this! Two ways to write W 1 W  CV 2 2 16 3.2 Energy storage in capacitors: Where is the Energy Stored? • Energy is stored in the electric field itself Think of the energy needed to charge the capacitor as being the energy needed to create the field • To calculate . 2 Chapter IX Conductors, Capacitors §1. Charges and electric field on conductors §2. Capacitance of conductors and capacitors §3. Energy storage in capacitors. the charge density is small 2/20/2008 6 §2. Capacitance of conductors and capacitors: 2.1 Charging by induction: A charge body (rod) can give another