{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# hw4 - ECE604 Homework 4 Out Tuesday February 1 2005 Due...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ECE604 Homework 4 Out: Tuesday, February 1, 2005 Due: Tuesday, February 8, 2005 Problems given by number are from the text by Ramo, Whinnery and Van Duzer (3rd edition, 1994). 1) 7.12h Also give an expression for the added capacitance per unit length AND evaluate numerically. Hints: a) Use a superposition solution (I) = (131 + (1)2, where (131 = Voy/ a is the solution for the parallel plate capacitor without the extra conducting strip. b) In solving for (1)2, solve separately for x 2 0 and x S 0. Once you have the solution for x 2 0, the solution for x S 0 follows almost by inspection. c) Use your solution for (132 in computing the added capacitance. 2) a) Shown below are two infinitely long, very thin insulated conducting plates which are held at potentials V0 and 0 as indicated. (The plates are infinite in the z—direction and semi—infinite in the other dimension.) qr)“ YT \ q <1) 05‘. \| —_.______l_..__.__ _L__> V=0 x Determine the potential distribution for 0 < (j) < 0L and for 06 < q) < 21:. b) Shown below are two infinitely long, very thin conducting plates separated by a dielectric of permittivity 8, which are held at potentials V0 and 0 as indicated. (The plates are infinite in the z—direction and finite in the x—y plane.) 3) 4) (i) Neglecting the effects of fringing, determine the capacitance of the structure per unit length. (ii) Neglecting the effects of fringing and without using the relationship WE = A C V2 , determine the energy stored in the structure per unit length. Show that your result is in fact equal to %C V2. A solid dielectric cylinder of radius a and length 2L is uniformly polarized with polarization P, where P is directed axially (i.e. P 2 p2 ; where p = const.). Determine the electric field, E, along the cylinder axis inside and outside of the cylinder (i.e. E(Z) |X:y:0 ). Hint: Identify the bound charge at the surfaces. These bound charges act as a source for E, which can be obtained through integration. A sphere of radius a has electric charge distributed on its surface so that the electric field inside is uniform and given by Ei 2 E02 (for r < a) The sphere is hollow, i.e. e = 80 everywhere inside the sphere. The sphere is embedded in an insulator, with dielectric constant 8. a) Determine the surface charge density ps(9) on the surface of the sphere. Hint: First solve for the potential using Laplace’s equation and appropriate boundary conditions. 5) 6) 7) 8) 9) b) Make a sketch showing representative E—field lines and the distribution of surface charge. Comment on the behavior of the field lines at the boundary. 2.3b 2.30 2.4b Also find H4, (r) outside the beam. 2.46 2.5 ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 3

hw4 - ECE604 Homework 4 Out Tuesday February 1 2005 Due...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online