Question

Two similar spheres having $+ q$ and $- q$ charge are kept at a certain distance.$F$force acts between the two. If in the middle of two spheres, another similar sphere having $+ q$ charge is kept, then it experience a force in magnitude and direction as

• A. Zero having no direction
• B. $8F$ towards $+ q$ charge
• C. $8F$ towards$- q$ charge
• D. $4F$ towards $+ q$ charge

Answer 1

Answer: (C)

$8F$ towards$- q$ charge

Answer 2

Initially, force between A and C $F = k\frac{Q^{2}}{r^{2}}$

When a similar sphere B having charge +Q is kept at the mid point of line joining A and C, then Net force on B is $F_{net} = F_{A} + F_{C} = k\frac{Q^{2}}{\left( \frac{r}{2} \right)^{2}} + \frac{kQ^{2}}{\left( \frac{r}{2} \right)^{2}} = 8\frac{kQ^{2}}{r^{2}} = 8F$.

(Direction is shown in figure)