Question

Two small, identical 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)