Lecture03_Part2_V1.1

# Lecture03_Part2_V1.1 - PHY501 Lecture III—Part 2 Boundary...

This preview shows pages 1–4. Sign up to view the full content.

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

View Full Document

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: PHY501 Lecture III—Part 2 Boundary Conditions at the Interface Between Dielectrics V1.1 Dielectric Boundary Conditions It is often useful to expand the potential due to a localized charge distribution in terms of spherical harmonics Since E 2 E 1 ( ) ˆ n 21 = 0 (58) Thus E || is continuous at an interface. Since there are an infinite number of contours C—each of them perpendicular to n 21 , we write 2 n 1 D 2 Gaussian Surface 1 D 1 D ˆ n da S = Q enc D 2 ˆ n 21 ( ) A D 1 ˆ n 21 ( ) A = A D 2 D 1 ( ) ˆ n 21 = (56) For = 0, D is continuous E = E = E ( ) S ˆ n¡da = E d l = C by Stokes Theorem E 2 ( ) || d E 1 ( ) || d = 0 (57) Also, if we assume that is not infinite we have E 1 = 2 (59) d 2 1 1 2 Stokes Contour E E Dielectric Boundary Conditions Example I: Charge near a planar interface. D 1 = 1 4 q cos d 2 + s 2 q 'cos d 2 + s 2 = 1 4 q q ' ( ) d d 2 + s 2 ( ) 3 2 q 1 2 d We use the method of images. In effect, we have two image problems: one in region 1 and one in region 2. Recall that in image problems, all images must exist outside of the region of interest. In region 1, we see the real charge q and image q’, while in Region 2, we see only the image q’’. Region 2, we see only the image q’’....
View Full Document

{[ snackBarMessage ]}

### Page1 / 9

Lecture03_Part2_V1.1 - PHY501 Lecture III—Part 2 Boundary...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online