conductingsphere.pg

#DESCRIPTION
#ENDDESCRIPTION

##KEYWORDS('module 4','electric fields')

DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PG.pl",
"StdConst.pg",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl"
);

TEXT(&beginproblem);
# Use 0 if it is true or false
#     1 if it is a numerical answer
#
$showPartialCorrectAnswers = 0;

$image_name1 = "./sphereplate.gif";
$image_width1 = 140;
$image_height1 = 200;

$image_name2 = "./twospheres.gif";
$image_width2 = 170;
$image_height2 = 200;

$q = random(1.0, 3.0, 0.1);
$charge = $q * 1E-9;
$w = random(1.0, 4.0, 0.2);
$weight = $w * 1E-5;

$epsilon = 8.85E-12;
$k = 1/(4*$pi*$epsilon);

$angle = 20*$pi/180;
$Eforce = tan($angle) * $weight;

$Efield = $Eforce / $charge;

$r = sqrt($k* ($charge**2) / $Eforce);

$ans_a = $Eforce;
ANS(num_cmp($ans_a, units => 'N'));

$ans_a = $Efield;
ANS(num_cmp($ans_a, units => 'N/C'));

$ans_a = $r;
ANS(num_cmp($ans_a, units => 'm'));


BEGIN_TEXT
$BR
\{ image($image_name1, width => $image_width1, height => $image_height1) \}
$PAR
$PAR
A very small negatively-charged conducting sphere is suspended 
by an insulating thread from support S. 
It is placed close to a vertical metal plate carrying a positive charge. 
The sphere is attracted towards the plate and hangs with the thread at an 
angle of 20\(^{\circ}\) to the vertical as shown in the figure.

$PAR 
(a) The sphere of weight $w \(\times 10^{-5}\) N carries a charge of -$q \(\times 10^{-9}\) C. 
Find the magnitude of the attractive force between the sphere and the plate.

$PAR
\( F = \) \{ ans_rule(20) \}

$PAR
(b) Determine the magnitude of the electric field strength at the sphere, 
treated as a point charge.

$PAR
\( E = \) \{ ans_rule(20) \}

$PAR

$PAR
(c) The plate is removed. The diagram below shows an identical sphere 
carrying a charge of +$q \(\times 10^{-9}\) C, mounted on an insulating stand.
It is placed so that the hanging sphere remains at 20\(^{\circ}\) to the vertical. 
Treating the spheres as point charges, calculate the distance r between their centres.

$BR
\{ image($image_name2, width => $image_width2, height => $image_height2) \}
$PAR
\( r = \) \{ ans_rule(20) \}



END_TEXT


ENDDOCUMENT();        # This should be the last executable line in the problem.