Question 765: Electrostats & Capacitance

Question

Two equally charged small balls placed at a fixed distance experience a force ' $F$ '. A similar uncharged ball after touching one of them is placed at the middle point between the two balls. the force experienced by this ball is

Accepted Answer

In the first case:
$$ F=K \frac{q^2}{r^2} 	ext { where, } K=\frac{1}{4 \pi \varepsilon_0} $$
When uncharged ball is touched to one of the balls, the charge $q$ is equally shared by them.
Hence each has charge $\frac{\mathrm{q}}{2}$.
The forces on the middle ball due the two balls are opposite in direction. The resultant force in given by
$$ \begin{aligned} F^{\prime}=K \frac{q \cdot \frac{q}{2}}{\left(\frac{r}{2}ight)^2}-K \frac{\frac{q}{2} \cdot \frac{q}{2}}{\left(\frac{r}{2}ight)^2} & =K\left(\frac{2 q^2}{r^2}-\frac{q^2}{r^2}ight) \ & =K \frac{q^2}{r^2}=F \end{aligned} $$

Answer

$\frac{\mathrm{F}}{2}$

Answer

F

Answer

2 F

Answer

4 F

Electrostats & Capacitance

Two equally charged small balls placed at a fixed distance experience a force ' F '. A similar uncharged ball after touching one of them is placed at the middle point between the two balls. the force experienced by this ball is

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