Two identical metallic spheres A and B when placed at certain… | JEE Main 2022 (29 Jul, Shift 2)

Q46JEE Main 2022 · 29 JUL · SHIFT 2Medium

Electric Charge & Coulomb's Law

Two identical metallic spheres $A$ and $B$ when placed at certain distance in air repel each other with a force of $F$ . Another identical uncharged sphere $C$ is first placed in contact with $A$ and then in contact with $B$ and finally placed at midpoint between spheres A and B. The force experienced by sphere C will be:

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Answer: (b)

Let each charge be $q$ , $F = \dfrac{kq^2}{r^2}$ . After contacts: $A = \dfrac{q}{2}$ , $B = C = \dfrac{3q}{4}$ .
C at midpoint, distance $r/2$ from each. Force from A on C $= \dfrac{k(q/2)(3q/4)}{r^2/4} = \dfrac{3}{2}F$ (towards B).
Force from B on C $= \dfrac{k(3q/4)^2}{r^2/4} = \dfrac{9}{4}F$ (towards A).
Net $= \dfrac{9}{4}F - \dfrac{3}{2}F = \dfrac{3}{4}F$ . So the answer is (b) $3F/4$ .

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