BOUNDARY VALUE PROBLEMS WITH DIELECTRICS
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)
A)
i and iii B) ii and iv
C) i and ii D) iii and iv
E) Some other combination!
4.10
a
Region 1 (
)
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
)?
Region 2 (
)
2
1
E
2
E
1
A)
Done with I
B)
Not yet…
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.
4.2
a
Now what if the sphere is a dielectric?
How do you expect the bound surface
charge to depend on the polar angle
(
)?
a)
Uniform + on top half,
uniform – on bottom
b)
cos(
)
c) Nothing simple, it yields an infinite series of
cos
’
s with coefficients
.
4.2
b
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...
4.10
b
A) B)
C) D)
E) None of these, or MORE than one...
4.10
You have a boundary between two linear dielectric
materials (
r
has one value above, another below, the
boundary) Define
r
Choose the correct formula(s) for V at the boundary
WRITTEN BY: Steven Pollock (CU-Boulder)
Explore concepts of dielectrics in boundary value problems, understanding continuity of electric fields and surface charges across boundaries between different materials. Investigate relationships between field orientations and surface charges in uniform and dielectric spheres.
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Presentation Transcript
4.10 a You have a straight boundary between two linear dielectric materials ( rhas 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) A) i and iii B) ii and iv C) i and ii D) iii and iv E) Some other combination!
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)? A) Done with I B) Not yet 2 Region 2 ( ) E2 1 E1 Region 1 ( )
You put a conducting sphere in a uniform E-field. How does the surface charge depend on the polar angle ( )? 4.2 a 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.
4.2 b Now what if the sphere is a dielectric? How do you expect the bound surface charge to depend on the polar angle ( )? a) Uniform + on top half, uniform on bottom b) cos( ) c) Nothing simple, it yields an infinite series of cos s with coefficients.
4.10 b 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 Vout-Vin=-stot A) B) Vout-Vin= 0 e0 eoutVout-einVin= -stot C) D) eoutVout-einVin= 0 e0 E) None of these, or MORE than one...
4.10 You have a boundary between two linear dielectric materials ( r has one value above, another below, the boundary) Define = r Choose the correct formula(s) for V at the boundary V nout V nin = tot 0 = free 0 V V A) B) nout nin eout V -ein V V nout V nin C) D) nout =-sfree out in = bound nin E) None of these, or MORE than one...
