Summary of Apr. 4, 2007


	Boundary, capacitance and Laplace Eqn	Apr. 4, 2007

+ Boundary conditions at 2 different media:
tangential component: [equation]
normal component:
step: 1) identify normal to the boundary ( goes from medium 2 to 1),
2) get the or at the boundary by substituting equation of the boundary,
3) apply boundary conditions component by component

+ Capacitance C=q/V (Sect. 3.9)
step: 1) Assume +q on one plate and -q on the other,
2) find [equation] for the given charge distribution,
3) relative potential of 2 plates and find C (F)

Example 3.12: Parallel plate capacitor
Example 3.13: Capacitance of a cylindrical capacitor

parallel capacitor = [equation]
series capacitor =
Example 3.15: Capacitance of a split dielectric

+ Electrostatic energy: (Sect. 3.10.1)
density [equation]
energy
Example 3.14: Energy stored in a cylindrical capacitor

+ Recap: capacitance C=q/V (pp. 116-126)
Boundary conditions (Sect. 3.8)
Polarization and dielectric (pp. 102-107)

+ Method of image (Sect. 3.11.5)
Charge in front of a grounded conductive planes is similar to an object facing a mirror.
The whole system can be replaced by an "equivalent charge diagram" with real and image charges.
Image charge has opposite charge of the real one and locates behind the conductor.
Equivalent diagram is valid for the space occupied by the real charge(s), i.e. in front of the conductor.
Example 3.16: charge above a grounded plate

+ Poisson's equation (Sect. 3.11.1): [equation] .
Relating (free volume) charge density and potential.
Apply to regions with uniform permittivity, e.g. semi-conductors (diode)

+ Laplace's equation: For region without free charges, Laplace's equation [equation] holds e.g. capacitors.
Example 3.17: Potential of a parallel plate capacitor
______________________________________

HW #17 (no late homework)	Due 4/10/07

1. Problem 3.8 (page 144). Before finding the answer, write down the number of regions. (Notice [equation]

is unchanged for R>b.)
2. i) Problem 3-14 a) (find the densities for bounded charges) only (page 145) and ii) in a slab of dielectric material for which [equation]

and

V, find a) [equation]

and

, b)

and

.
3. Assume that the z=1 plane separates two lossless dielectric regions with [equation]

and

. If we know that [equation]

in region 1 is [equation]

, what are the expressions for [equation]

and

in region 2? Can we apply these expressions to the whole region 2? Explain. (modified Problem 3.18 on page 145) (Note: This a boundary problem. Do not forget to substitute the equation of the boundary.)
Extra-Credit
A 4cm glass sphere with relative permittivity [equation]

is placed in air with relative permittivity [equation]

. The electric field intensity in air [equation]

. i. Find the unit vector that is normal to the air-glass boundary; ii. Find electric field intensity, [equation]

and electric flux density, [equation]

inside the sphere at the air-glass boundary; iii. Find the bound surface charge density at the air-glass boundary.

Discussion in uwm.course.ee361