1. Does the average cost per cup of coffee served increase, decrease, or remain the same as the
number of cups of coffee served in a week increases?
Decrease

PROBLEM:
A point charge q is brought to a position a distance d away from an infinite plane conductor held at
zero potential. Using the method of images, find:
(a) the surface-charge density induced on the plane, and plot it;
(b) the force between the pla

In other problems where we must have a valid solution at the origin, Bl must be zero to keep the
solution from blowing up at the origin. But in this problem, we do not seek a valid solution at the
origin, so we cannot use this restriction.
Apply the bound

Now make the substitution 1/U in the first bracket, 2/V in the second bracket, and
3/W in the last bracket. We can do this as long as we let 1, 2, and 3 go to zero just like we were
letng go to zero. D=[ e uu ' 2 / 21 2 2 1 ][ e vv ' 2 /2 2 2 2 2 ][ e ww

The Kronecker delta makes every term in the sum collapse to zero except when l = l'
0
V1 Pl
cossin d =Al a
lBl a
l1
2
2 l1
Flip the equation and plug in the explicit form of V1
Al a
lBl a
l1=
2l1
2
V
0
/ 2
Pl
cossin d
Make a change of variables: x=cos ,

Again, this should be obvious that this is the surface charge density time the delta, where the surface
charge density is the linear charge density divided by the circumference of the cylinder.
(c) For the flat disc, we must use the step function H in the

Because of the spherical geometry of the problem and the absence of charge, we choose to solve the
Laplace equation in spherical coordinates:
2=0
1
r
2
r
2
r
1
r
2
sin
sin
1
r
2
sin2
2
2=0
Using the method of separation of variables leads to the g

The two equations in boxes form a system of equations that we can solve for Al and Bl.
Al=
a
l11
l
b
l1
a
2 l1b
2 l1
2 l1
2
V
0
1
Pl
x dx
Bl=
a
l1
b
2l11
l
a
2 l1
b
l1
a
2l1b
2 l1
2l1
2
V
0
1
Pl
x dx
The final solution is then:
r , ,=
V
2
l
2l1
0
1
Pl

PROBLEM:
The Dirac delta function in three dimensions can be taken as the improper limit as 0 of the
Gaussian function
D ; x , y ,z=2
3/ 2
3
exp[
1
2
2
x
2y
2z
2
]
Consider a general orthogonal coordinate system specified by the surfaces u = constant, v =

Expand the arc length in the new coordinate system: D= 2 3/ 2 3 exp[ 1 2 2 du2 U 2 dv2 V
2 dw2 W 2 ] Note that dxdu/U and we are not making that claim here. Rather, the entre threedimensional incremental arc length ds is the same in all orthogonal coordin

PROBLEM:
Using Dirac delta functions in the appropriate coordinates, express the following charge distributions as
three-dimensional charge densities (x).
(a) In spherical coordinates, a charge Q uniformly distributed over a spherical shell of radius R.
(

Use the orthogonality condition of Legendre polynomials:
0
Pl '
cos Pl
cos sin d =
2
2l1
l 'l
Al b
lBl b
l1=
2 l1
2
0
V 2 Pl
cossin d
Plug in the explicit form of V2
Al b
lBl b
l1=
2 l1
2
V
/ 2
Pl
cossin d
Make a change of variables: x=cos , dx=sin d

1.Award:10 out of 10.00 pointsShow correct answerThe PC Works assembles custom computers from
components supplied by various manufacturers. Thecompany is very small and its assembly shop and
retail sales store are housed in a single facility in aRedmond,

Direct materials:Raw materials inventory, beginning$12,000Add: Purchases of raw materials30,000Total
raw materials available42,000Less: Raw materials inventory, ending18,000Raw materials used in
production24,000Less: Indirect materials included in manufac

Primare CorporationSchedule of Cost of Goods SoldFinished goods inventory, beginning$35,000Add:
Cost of goods manufactured155,000Goods available for sale190,000Less: Finished goods inventory,
ending42,000Unadjusted cost of goods sold148,000Add: Underappli

Direct materials:Raw materials inventory, beginning$20,000Add: Purchases of raw materials400,000Raw
materials available for use420,000Less: Raw materials inventory, ending30,000Raw materials used in
production390,000Less: Indirect materials15,000$375,000D

Direct materials:Raw materials inventory, beginning$40,000Add: Purchase of raw materials290,000Raw
materials available330,000Less: Raw materials inventory, ending10,000Raw materials used in
production$320,000Direct labor78,000Manufacturing overhead applie

Finished goods inventory, beginning$50,000Add: Cost of goods manufactured690,000Cost of goods
available for sale740,000Less: Finished goods inventory, ending80,000Unadjusted cost of goods
sold660,000Less: Overapplied overhead15,000Adjusted cost of goods s

1.
Award: 10 out of 10.00 points
Show correct answer
The PC Works assembles custom computers from components supplied by various manufacturers. The
company is very small and its assembly shop and retail sales store are housed in a single facility in a
Red

.Depreciation on salespersons cars.Period cost2.Rent on equipment used in the factory.Product
cost3.Lubricants used for machine maintenance.Product cost4.Salaries of personnel who work in the
finished goods warehouse.Period cost5.Soap and paper towels use

.Depreciation on salespersons cars.Period cost2.Rent on equipment used in the factory.Product
cost3.Lubricants used for machine maintenance.Product cost4.Salaries of personnel who work in the
finished goods warehouse.Period cost5.Soap and paper towels use

PROBLEM:
Calculate the multipole moments qlm of the charge distributions shown as parts a and b. Try to obtain
results for the non-vanishing moments valid for all l, but in each case find the first two sets of
nonvanishing
moments at the very least.
(a) (