1. Tardigrade
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  4. Two equally charged, identical metal spheres A and B repel each other with a force F. The spheres are kept fixed with a distance r between them. A third identical, but uncharged sphere C is brought in contact with A and then placed at the mid-point of the line joining A and B. The magnitude of the net electric force on C is

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Q. Two equally charged, identical metal spheres $A$ and $B$ repel each other with a force $F$. The spheres are kept fixed with a distance $r$ between them. A third identical, but uncharged sphere $C$ is brought in contact with $A$ and then placed at the mid-point of the line joining $A$ and $B$. The magnitude of the net electric force on $C$ is

Electric Charges and Fields

Solution:

Initially,
image
$F=k \frac{Q^{2}}{r^{2}}$ ......(i)
Finally,
image
Force on $C$ due to $A, F_{A}=\frac{k(Q / 2)^{2}}{(r / 2)^{2}}=\frac{k Q^{2}}{r^{2}}$
Force on $C$ due to $B, F_{B}=\frac{K Q(Q / 2)}{(r / 2)^{2}}=\frac{2 K Q^{2}}{r^{2}}$
$\therefore $ Net force on $C, F_{n e t}=F_{B}-F_{A}=\frac{k Q^{2}}{r^{2}}=F$