IMAT 2023 · Question 60

Q60 - Electrostatics

Two perfectly insulating spheres charged respectively with Q₁ and Q₂ and with a respective radius of R₁ and R₂ are placed in contact. What will the charge on the sphere of radius R₁ now be? A) Q₁ B) Q₂ C) (Q₁R₁² + Q₂R₂²)/(R₁² + R₂²) D) 0 E) (Q₁R₁ + Q₂R₂)/(R₁ + R₂)
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The correct answer is A) Q₁.

The spheres are perfect insulators, so charge can't move through them and nothing flows from one to the other when they touch. Each keeps the charge it started with: Q₁.

Option E is the answer for conducting spheres, where charge spreads out in proportion to the radii. Insulator versus conductor is the whole point of the question.

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