Lecture 7 Practice Problems

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Lecture 7 Practice Problems

• Prof. Viviana Vladutescu

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Divergence Theorem and Gausss Law
Suppose D 6rcos f af C/m2.(a) Determine the
charge density at the point (3m, 90?, -2m). Find
the total flux through the surface of a
quartered-cylinder defined by 0 r 4m, 0
f 90?, and -4m z 0 by evaluating (b) the
left side of the divergence theorem and (c) the
right side of the divergence theorem. (a)
(b)
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note that the top, bottom and outside integrals
yield zero since there is no component of D in
the these dS directions.
So,
(c)
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Electric Potential
The potential field in a material with er 10.2
is V 12 xy2 (V). Find E, P and D.
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Boundary Conditions
For z 0, er1 9.0 and for z gt 0, er2 4.0.
If E1 makes a 30? angle with a normal to the
surface, what angle does E2 make with a normal to
the surface?
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Therefore
also
and after routine math we find
Using this formula we obtain for this problem q2
14.
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1. A spherical capacitor consists of a inner
conducting sphere of radius R13cm, and surface
charge density ?s2nC/m2 and an outer conductor
with a spherical inner wall of radius R25cm .
The space in between is filled with
polyethylene. a) Determine the electric field
intensity from ?s between plates(15 points) b)
Determine the voltage V12 (10 points) c)
Determine the capacitance C (10 points) 2.
Consider a circular disk in the x-y plane of
radius 5.0 cm. Suppose the charge density is a
function of radius such that ?s 12r nC/cm2
(when r is in cm). Find the electric field
intensity a point 20.0 cm above the origin on the
z-axis.(25 points)
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3. Assume the z0 plane separates two lossless
dielectric regions, where the first one is air
and the second one is glass. If we know that the
electric field intensity in region 1 is E1 2y ax
-3x ay(5z) az, a)Find E2 and D2 at the
boundary side of region 2? (20 points) b)Can we
determine E2 and D2 at any point in region 2?
Explain.(5 points) 4. Two spherical conductive
shells of radius a and b (b gt a) are separated by
a material with conductivity s. Find an
expression for the resistance between the two
spheres.(20 points)
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Problem 2
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Problem 3
At the z0 plane
From the boundary condition of two dielectrics we
get
12
z0
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Problem 4- Hint
l
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Resistance of a straight piece of homogeneous
material of a uniform cross section for steady
current
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Resistances connected in series
Resistances connected in parallel
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Problem 4
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