Question

A and B are two identically spherical charged bodies which repel each other with force F, kept at a finite distance. A third uncharged sphere of the same size is brought in contact with sphere B and removed. It is then kept at mid point of A and B. Find the magnitude of force on C.:

• A. $\frac{F}{2}$
• B. $\frac{F}{8}$
• C. $F$
• D. Zero

Answer 1

The correct option is C $F$

From the figure again we can conclude that $C$ is placed at $\frac{r}{2}$.

Now, see the direction of force due to $A$ on $C$. $F_{AC}$ and force due to $B$ on $C$, $F_{BC}$

$F_{AC}=\frac{KQ\frac{Q}{2}}{\frac{r^2}{4}}=\frac{2QK}{r^2}=2F$

$F_{BC}=\frac{K\frac{Q^2}{4}}{\frac{r^2}{4}}=\frac{{KQ}^2}{r^2}=F$

The resultant force according to diagram will be

$F_{resultant}=2F-F=F$ along $F_{AC}$