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← JEE Main 2022 · 29 Jul · Shift 2
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JEE Main 2022 · 29 Jul · Shift 2, Physics question 31

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:

Choose one option
Answer and worked solution

Official answer: B

Charges. A and B start with q each. After touching A, C has q2\frac q2; after touching B, C and B each have 3q4\frac{3q}4; A keeps q2\frac q2.

At the midpoint the two repulsions oppose: FC=k⋅3q4(3q4−q2)(d/2)2=3kq24d2=3F4F_C=\dfrac{k\cdot\frac{3q}4\left(\frac{3q}4-\frac q2\right)}{(d/2)^2}=\dfrac{3kq^2}{4d^2}=\dfrac{3F}4.

(B)

Topics:Coulomb's law and superposition
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