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Two identical spheres A and B are equally charged and seperated by a certain distance. Another identical uncharged sphere C is brought in contact with A and then placed mid way between A and B,. Calculate the resultant force on C if initial force between A and B is 2*10^-5 N.

Two identical spheres A and B are equally charged and seperated by a certain distance. Another identical uncharged sphere C is brought in contact with A and then placed mid way between A and B,. Calculate the resultant force on C if initial force between A and B is 2*10^-5 N.

Grade:12

2 Answers

Eshan
askIITians Faculty 2095 Points
4 years ago
Let the distance between the charges berand their charges beqeach.

Hence the force between them is\dfrac{kq^2}{r^2}=2\times 10^{-5}N

When identical uncharged sphere is brought in contact, the charge on the charged sphere gets divided equally. Hence charge on both A and C becomes\dfrac{q}{2}.
Hence force on C due to A after it is moved to the mid point=\dfrac{k(\dfrac{q}{2})(\dfrac{q}{2})}{(\dfrac{r}{2})^2}=\dfrac{kq^2}{r^2}=F

Force on C due to B=\dfrac{kq(\dfrac{q}{2})}{(\dfrac{r}{2})^2}=\dfrac{2kq^2}{r^2}=2F
Hence net force on C=2F-F=F
Gitanjali Rout
184 Points
4 years ago
Hence net force on C=2F-F=F\dfrac{kq(\dfrac{q}{2})}{(\dfrac{r}{2})^2}=\dfrac{2kq^2}{r^2}=2FForce on C due to B=\dfrac{k(\dfrac{q}{2})(\dfrac{q}{2})}{(\dfrac{r}{2})^2}=\dfrac{kq^2}{r^2}=F.Hence force on C due to A after it is moved to the mid point=\dfrac{q}{2}When identical uncharged sphere is brought in contact, the charge on the charged sphere gets divided equally. Hence charge on both A and C becomes\dfrac{kq^2}{r^2}=2\times 10^{-5}Neach.Hence the force between them isqand their charges berLet the distance between the charges be
thanks

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