Transcript Dielectric
W05D2 Dielectrics and Conductors as Shields Today’s Reading Assignment: Course Notes Sections 5.4, 5.6, 5.8-5.9 1 Announcements Math Review Week 06 Tuesday 9-11 pm in 26-152 PS 5 due W05 Tuesday at 9 pm in boxes outside 32082 or 26-152 Add Date Week 05 Friday W05D3 Reading Assignment: Friday Problem Solving Capacitance and Dielectrics Course Notes Sections 5.6, 5.8-5.9 2 Outline Dielectrics Electric Fields in Matter Conductors as Shields 3 Capacitors and Dielectrics 4 Dielectrics A dielectric is a non-conductor or insulator Examples: rubber, glass, waxed paper When placed in a charged capacitor, the dielectric reduces the potential difference between the two plates HOW??? 5 Molecular View of Dielectrics Polar Dielectrics : Dielectrics with permanent electric dipole moments Example: Water 6 Molecular View of Dielectrics Non-Polar Dielectrics Dielectrics with induced electric dipole moments Example: CH4 7 Dielectric in Capacitor Potential difference decreases because dielectric polarization decreases Electric Field! 8 Dielectric Constant Dielectric weakens original field by a factor e = ke 0 E k E0 Dielectric Constant Dielectric constants Vacuum 1.0 Paper 3.7 Pyrex Glass 5.6 Water 80 9 Group Problem: Induced Surface Charge Density A dielectric material with constant k completely fills the space between two conducting plates that have a surface charge densities ±s as shown in the figure. Induced surface charge densities ±s ind appear on the surfaces of the dielectric. Find an expression for s ind in terms of k and s . 10 Demonstration: Parallel Plate Capacitor with Dielectric E5 http://tsgphysics.mit.edu/front/?page=demo.php&letnum=E%205&show=0 11 Dielectric in a Capacitor Q0 = constant after battery is disconnected Upon inserting a dielectric free charge on plates does not change, potential decreases, capacitance increases V0 Q0 Q0 Q V C C0 V V0 / V0 12 Dielectric in a Capacitor V0 = constant when battery remains connected Q CV C0V0 Upon inserting a dielectric free charge on plates increase Q Q0 13 Gauss’s Law with Dielectrics In both cases: E d A S qfree,in 0 14 Concept Questions: Dielectric in a Capacitor 15 Concept Question: Dielectric A parallel plate capacitor is charged to a total charge Q and the battery removed. A slab of material with dielectric constant k is inserted between the plates. The charge stored in the capacitor + + + + + + + + k - - - - - - - - 1. Increases 2. Decreases 3. Stays the Same 16 Concept Question Answer: Dielectric Answer: 3. Charge stays the same + + + + + + + + k - - - - - - - - Since the capacitor is disconnected from a battery there is no way for the amount of charge on it to change. 17 Concept Question: Dielectric A parallel plate capacitor is charged to a total charge Q and the battery removed. A slab of material with dielectric constant k in inserted between the plates. The energy stored in the capacitor + + + + + + + + k - - - - - - - - 1. Increases 2. Decreases 3. Stays the Same 18 Concept Question Answer: Dielectric Answer: 2. Energy stored decreases The dielectric reduces the electric field and hence reduces the amount of energy stored in the field. The easiest way to think about this is that the capacitance is increased while the charge remains the same so 2 U Q / 2C Also from energy density: uE ,0 2 E 1 1 2 0 E 0 uE ,0 2 2 19 Concept Question: Dielectric A parallel plate capacitor is charged to a total charge Q and the battery removed. A slab of material with dielectric constant k in inserted between the plates. The force on the dielectric + + + + + + + + k - - - - - - - - 1. pulls in the dielectric 2. pushes out the dielectric 3. is zero 20 Concept Question Answer: Dielectric Answer: 1. The dielectric is pulled in We just saw that the energy is reduced by the introduction of a dielectric. Since systems want to reduce their energy, the dielectric will be sucked into the capacitor. Alternatively, since opposing charges are induced on the dielectric surfaces close to the plates, the attraction between these will lead to the attractive force. 21 Conductors as Shields 22 Concept Question: Point Charge Inside Conductor 23 Concept Question: Point Charge in Conductor A point charge +Q is placed inside a neutral, hollow, spherical conductor. As the charge is moved around inside, the surface charge density on the outside 1. 2. 3. 4. is initially uniform and does not change when the charge is moved. is initially uniform but does become non-uniform when the charge is moved. is initially non-uniform but does not change when the charge is moved. is initially non-uniform but does change when the charge is moved. 24 Concept Question Answer: Q in Conductor Answer: 1 is initially uniform and does not change when the charge is moved. E = 0 in conductor -Q on inner surface Charge conserved +Q on outer surface E = 0 in conductor No “communication” between –Q & +Q + Q uniformly distributed 25 Concept Question: Point Charge in Conductor A point charge +Q is placed inside a neutral, hollow, spherical conductor. As the charge is moved around inside, the electric field outside 1. 2. 3. 4. +Q is zero and does not change is non-zero but does not change is zero when centered but changes is non-zero and changes 26 Concept Question Answer: Q in Conductor Answer: 2. is non-zero but does not change. E = 0 in conductor -Q on inner surface Charge conserved +Q on outer surface E = 0 in conductor No “communication” between –Q & +Q + Q remains uniformly distributed so E stays unchanged 27 Shielding By Conducting Shell: Applet Charge placed INSIDE induces balancing charge ON INSIDE. Electric field outside is field of point charge. http://web.mit.edu/viz/EM/visualizations/electrostatics/ChargingByInduction/shielding/shielding.htm 28 Shielding by Conducting Shell: Applet Charge placed OUTSIDE induces charge separation ON OUTSIDE. Electric field is zero inside. http://web.mit.edu/viz/EM/visualizations/electrostatics/ChargingByInduction/shielding/shielding.htm 29 Demonstration: Faraday Cage D33 http://tsgphysics.mit.edu/front/?page=demo.php&letnum=D%2033&show=0 30 Experiment 1 Faraday Ice Cage 31