Capacitors and Dielectrics

1. Capacitors and Dielectrics Sub Name : Engineering Chemistry Prepared By S.Karthik, M.Sc., M.Phil., Assistant Professor / Chemistry 1

2. 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???

3. Molecular View of Dielectrics Polar Dielectrics : Dielectrics with permanent electric dipole moments Example: Water

4. Molecular View of Dielectrics Non-Polar Dielectrics Dielectrics with induced electric dipole moments Example: CH4

5. Dielectric in Capacitor Potential difference decreases because dielectric polarization decreases Electric Field!

6. Dielectric Constant Dielectric weakens original field by a factor Dielectric Constant Dielectric constants Vacuum 1.0 Paper 3.7 Pyrex Glass 5.6 Water 80

7. Group Problem: Induced Surface Charge Density A dielectric material with constant completely fills the space between two conducting plates that have a surface charge densities as shown in the figure. Induced surface charge densities appear on the surfaces of the dielectric. Find an expression for in terms of and .

8. 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

9. Dielectric in a Capacitor V0 = constant when battery remains connected Upon inserting a dielectric free charge on plates increase

10. Gauss’s Law with Dielectrics In both cases:

11. Concept Questions:Dielectric in a Capacitor

12. + + + + + + + + - - - - - - - - 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 is inserted between the plates. The charge stored in the capacitor • Increases • Decreases • Stays the Same

13. + + + + + + + + - - - - - - - - Concept Question Answer: Dielectric Answer: 3. Charge stays the same Since the capacitor is disconnected from a battery there is no way for the amount of charge on it to change.

14. + + + + + + + + - - - - - - - - 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 in inserted between the plates. The energy stored in the capacitor • Increases • Decreases • Stays the Same

15. 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 Also from energy density:

16. + + + + + + + + - - - - - - - - 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 in inserted between the plates. The force on the dielectric • pulls in the dielectric • pushes out the dielectric • is zero

17. 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.

18. Conductors as Shields

19. Concept Question:Point Charge Inside Conductor

20. 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 • 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.

21. 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

22. +Q 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 • is zero and does not change • is non-zero but does not change • is zero when centered but changes • is non-zero and changes

23. 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

24. 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

25. 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