Question

A metal disk with a charge $Q_1=-1e$ is placed near a metal sphere that has a charge $Q_2=-4e$. If the disk touched the sphere, what is the possible final charge on each object?

• A. $Q_1=-2e,Q_2=-3e$
• B. $Q_1=-3e,Q_2=-3e$
• C. $Q_1=-1e,Q_2=+7e$
• D. $Q_1=-2e,Q_2=-2e$

Answer 1

The correct option is A $Q_1=-2e,Q_2=-3e$

Given that,
$Q_1=-1e$
$Q_2=-4e$
Considering (disc + sphere) as a system, total initial charge on the system is:
$q_i=Q_1+Q_2=-1e-4e$
$\Rightarrow q_i=-5e$
When the disc and sphere touches each other, redistribution of charges will take place.
However, as per conservation of charge, final charge on the system will remain same.
$\Rightarrow q_i=q_f=-5e$
Thus, $q_f=Q_1+Q_2=-5e$ is feasible only in option (a)

$\begin{array}{c}\text{Why this question ?}\\ \text{Tip: By considering (disc + sphere) as a system,}\\ \text{we can apply charge conservation on it.}\\ \text{Concept: The system is isolated, because it is not}\\ \text{connected to external source of charge.}\end{array}$