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(PHYS223)PHYS223MD.pdf
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I. A charge distribution p(r) generates the following field -.1.
E =-L.-";
~1IW.rl -=-~-:-J:::=---f.Vr1f.? e~"r+---~ ~-=-I--:-
where b is a col18!8nt. What is the charge density per) in space? What is the total
charge over the entire space? Remember to check your answer with Gauss law.

(20 points) -=-:--~ -----;..~ 4<fr:?7e-~~Tl,(nckT--b ,=1---. 1'--"-'-3~1'-br' q.b e-br._

'--~'-=' .-~S.(-rJ~._.~ 4-7((1. --
2. Find the electric field E and electric potential V inside and outside a sphere of radi us R which camea a charge density invenely proportional to the squared .
_.. 3~~b -br .-
distance crom the origin, p(r)=A:/,.J, where k is a constant, in addition to a point
charge q at the center. What is the total charge in the sphere? What is the total +----=-~7 -4'IC y2. e -
..
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energy stored in the system? Use infinity as the potentialrefercnce point. (25
points)
3. Two semi-infinite grounded conducting planes meet at an angle of 60.. In the
region between them, there is a point charge q, situated as shown. Set up the --.
~=--~~~~==_. ===t==
image charge configuration, and calculate the potential in the region. What is the
force acting on this charge by the induced charges on the two conducting planes?
(25 points)
--. ~-tdt -~f' ~2.e bry'SmOJ.n1o-r1:rp
-
-=i-=-tbf e-brol-f. .-..
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q ~~~1
y
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--~--
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4. A specified charge density 0(9)=00+3 e.,cos9 is glued over the surface of a -.-. spherical shell of mdius R. Note, your boundary condition at the spherical shell is -
-
not given by the potential itself. Rather, the given charge density can relate the
potential and its derivatives inside and outside the spherical surface. (30 points) -._.

(a)
Write down the ajJpropriate Partial Differential
Equations for the potential inside and outside ~ -.


the sphere;
.-.-.


(b)
Write down all the boundary conditions; fI

(c)
Solve the boundary condition problem in the .
appropriate coordinatea system for the



potential; _.
(d) Findtheelectricfieldinsideandoutsidethe
sphere. . --._.
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( i L~=~~~~~~~~~+-
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