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Electricity and Magnetism

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Advanced Charge Conservation in a Set of Conductors

EANDM-MANMBY

A different electric charge is placed on each of four identical conducting spheres, as shown in the figure below.

“Timothy Black. Created for Albert.io. Copyright 2016. All rights reserved.”

The initial charges placed on the four spheres are:

$q_1 = +11\text{ mC}$
$q_2 = +3\text{ mC}$
$q_3 = -6\text{ mC}$
$q_4 = +4\text{ mC}$

First, sphere one is placed in contact with sphere four. Then sphere two is placed in contact with sphere four. Next, charge sphere one is placed in contact with sphere three. Finally, sphere two is placed in contact with sphere three. In other words, we implement the following series of conduction events:

Step 1: Bring sphere one into contact with sphere four.
Step 2: Bring sphere two into contact with sphere four.
Step 3: Bring sphere one into contact with sphere three.
Step 4: Bring sphere two into contact with sphere three.

What are the charges on each of the four spheres following this series of conduction events?

A

$q_1 = +4.625\rm{ mC}$
$q_2 = +0.5\rm{ mC}$
$q_3 = +2.25\rm{ mC}$
$q_4 = +4.625\rm{ mC}$

B

$q_1 = +2.5\rm{ mC}$
$q_2 = +6\rm{ mC}$
$q_3 = +1\rm{ mC}$
$q_4 = +2.5\rm{ mC}$

C

$q_1 = +0.75\rm{ mC}$
$q_2 = +3\rm{ mC}$
$q_3 = +3\rm{ mC}$
$q_4 = +5.25\rm{ mC}$

D

$q_1 = +3\rm{ mC}$
$q_2 = +3\rm{ mC}$
$q_3 = +3\rm{ mC}$
$q_4 = +3\rm{ mC}$