$-$P$66$ Start with the program in Section $15\mathrm{.}9$ that calculates the electric field of a uniformly charged rod, modeled as $10$ point charges, at multiple observation locations in a circle around the rod. $($a$)$ Add more arrows to the list named "observation," so that the electric field of the rod is displayed with $5$ rings of

arrows centered on the rod, at different locations. $($b$)$ Increase the number of point charges used to model the rod to increase the accuracy of the calculation. Explain your criteria for determining an appropriate number of point charges.

STARTER CODE:

from vpython import $*$

scene.height $=800$

oofpez $=9$e$9$

Qtot$=1$e$-9$

L $=1$

N $=10$

dy $=$ L $/$ N

## Create a list of point charges

slices $=[]$ ## an empty list

i $=0$

y$0=-$L $/2+$ dy $/2$ ## center of bottom slice

while i $$ N:

a $=$ sphere $($pos $=$ vector $(0,$ y$0+$ i $*$ dy$,0),$ radius $=$ dy $/2,$

color $=$ color.red, q $=$ Qtot $/$ N$)$

slices.append$($a$)$ ## add sphere to list

i $=$ i $+1$

## Print index and position

i $=0$

while i $$ len$($slices$)$:

print$($i$,$ slices$[$i$].$pos$)$

i $=$ i $+1$

## Calculate E at observation location

r$\_$obs $=$ vector $(0\mathrm{.}05,0,0)$ ## to test calculation

E$\_$net $=$ vector $(0,0,0)$

i $=0$

while i $$ N:

rate $(100)$

r $=$ r$\_$obs $-$ slices$[$i$].$pos

rhat $=$ r$/$mag$($r$)$

E $=($oofpez $*$ slices$[$i$].$q $/$ mag$($r$)**2)*$ rhat

E$\_$net $=$ E$\_$net $+$ E

i $=$ i $+1$

print$($E$\_$net$)$

## Create a list of arrows

observation $=[]$

yobs $=0\mathrm{.}4$

dtheta $=2*$ pi $/12$ # Divide the circle into $12$ parts

theta $=0$

R $=0\mathrm{.}15$ ## radius of circle

while theta $<mtext></mtext><mn>2</mn><mtext></mtext><mi>*</mi>$ pi:

a $=$ arrow$($pos $=$ vector$($R $*$ cos$($theta$),$ yobs, R $*$ sin$($theta$)),$

color $=$ color.orange,

axis $=$ vector $(0,0,0))$

observation.append$($a$)$

theta $=$ theta $+$ dtheta

## Calculate E at observation location

sf $=0\mathrm{.}002$ ## arrow scale factor

for earrow in observation:

## Add E of all slices for this obs. loc.

E$\_$net $=$ vector$(0,0,0)$ # Reset E$\_$net for each arrow

for i in range$($N$)$:

r $=$ earrow.pos $-$ slices$[$i$].$pos

rhat $=$ r $/$ mag$($r$)$

E $=($oofpez $*$ slices$[$i$].$q $/$ mag$($r$)**2)*$ rhat

E$\_$net $=$ E$\_$net $+$ E

earrow.axis $=$ sf $*$ E$\_$net