question_answer

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                               [MP PET 1996]

A)                    Zero having no direction           

B)                    \[8F\] towards \[+\,q\] charge           

C)                    \[8F\] towards \[-\,q\] charge

D)                    \[4F\] towards \[+\,q\] charge

Correct Answer: C

Solution :

                     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 \[{{F}_{net}}={{F}_{A}}+{{F}_{C}}\]\[=k\frac{{{Q}^{2}}}{{{\left( {r}/{2}\; \right)}^{2}}}+\frac{k{{Q}^{2}}}{{{\left( {r}/{2}\; \right)}^{2}}}=8\frac{k{{Q}^{2}}}{{{r}^{2}}}=8F\]. (Direction is shown in figure)