Boundary value problems with dielectrics
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BOUNDARY VALUE PROBLEMS WITH DIELECTRICS

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Boundary value problems with dielectrics

BOUNDARY VALUE PROBLEMS WITH DIELECTRICS


Class activities

Class Activities


Boundary value problems with dielectrics

You have a straight boundary between two linear dielectric materials (r has one value above, another below, the boundary) There are no free charges in the regions considered. What MUST be continuous across the b’ndary?i) E(parallel) ii) E(perpendicular)iii) D(parallel) iv) D(perpendicular)

i and iii B) ii and iv

C) i and ii D) iii and iv

E) Some other combination!

4.10a


Boundary value problems with dielectrics

Two different dielectrics meet at a boundary. The E field in each region near the boundary is shown.There are no free charges in the region shown. What can we conclude about tan(1)/tan(2)?

Done with I

Not yet…

2

Region 2 (2)

E2

E1

1

Region 1 (1)


Boundary value problems with dielectrics

You put a conducting sphere in a uniform E-field. How does the surface charge depend on the polar angle ()?

a) Uniform + on top half, uniform – on bottom

b) cos()

c) sin()

d) Nothing simple, it yields an infinite series of cos’s with coefficients.

4.2a


Boundary value problems with dielectrics

Now what if the sphere is a dielectric? How do you expect the bound surface charge to depend on the polar angle ()?

Uniform + on top half, uniform – on bottom

cos()

c) Nothing simple, it yields an infinite series of cos’s with coefficients.

4.2b


Boundary value problems with dielectrics

You have a boundary between two linear dielectric materials (r has one value above, another below, the boundary) Choose the correct formula(s) for V at the boundary

A) B)

C) D)

E) None of these, or MORE than one...

4.10b


Boundary value problems with dielectrics

You have a boundary between two linear dielectric materials (r has one value above, another below, the boundary) Define =0rChoose the correct formula(s) for V at the boundary

A) B)

C) D)

E) None of these, or MORE than one...

4.10


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