Question

Two identical spheres carrying charges - 9 uC and 5 uC respectively are kept in contact and then separated from each other. Point out the true statement from the following. In each sphere
1) 1.25 $\times$ ${10^{13}}$ electrons are in deficit.
2) 1.25 $\times$ ${10^{13}}$ electrons are in excess.
3) 2.15 $\times$ ${10^{13}}$ electrons are in excess.
4) 2.15 $\times$ ${10^{13}}$ electrons are in deficit​.

Answer 1

Hint When two identical spheres are brought in contact to each other, the charges redistribute. And final charge on each sphere is given by Q = \[\dfrac{{{{\text{q}}_{\text{1}}}{\text{ + }}{{\text{q}}_{\text{2}}}}}{2}\]. Hence, now find out the number of electrons by using the formula = Magnitude of charge on each sphere / Charge on each electron to obtain the answer.

Complete step-by-step answer:
Given,
Two identical spheres carrying charges ${{\text{q}}_{\text{1}}}$ = -9 μC and ${{\text{q}}_{\text{2}}}$ = 5 μC respectively are kept in contact and then separated from each other.
When two identical spheres are kept in contact and then separated, their charges redistribute.
To find whether the electrons are in excess or deficit, we have to find out the net charge on the system i.e. Final charge on each sphere after they are separated.
Final charge on each of sphere, Q = \[\dfrac{{{{\text{q}}_{\text{1}}}{\text{ + }}{{\text{q}}_{\text{2}}}}}{2} = \dfrac{{ - 9 + 5}}{2} = - 2\mu C\]
Negative signs indicate that charge on each sphere is in excess . (Why? See Note at the end of answer)
So, number of electrons are in excess is given by,
  Magnitude of charge on each sphere / Charge on each electron. Hence, substituting values we have :
$
  \dfrac{{2\mu C}}{{1.6 \times {{10}^{ - 19}}}} \\
   \Rightarrow \dfrac{{2 \times {{10}^{ - 6}}C}}{{1.6 \times {{10}^{ - 19}}}} \\
   \Rightarrow 1.25 \times {10^{ - 13}} \\
 $

Therefore 1.25 $\times$ ${10^{13}}$ electrons are in excess.

Note Generally, we consider electrons excess when the overall charge (Q) on each sphere has a negative sign and since charge on electrons is negative; hence we say that electrons are in excess. Had they been positive, we could say that electrons are in deficit.