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A spherical conductor has two hollow cavities inside it. The conductor itself carries no net charge, but a charge q₁ is placed at the center of one cavity, and a charge q₂ is placed at the center of the other cavity. A third charge q₃ is located at a large distance r from the conductor. If the forces experienced by q₃, q₁, and q₂ are F₁, F₂, and F₃ respectively, which of the following is true? (Assume all charges are positive)
- F₁ is smaller than F₂, which is smaller than F₃
- F₁ equals F₂, but both are smaller than F₃
- F₁ equals F₂, but both are greater than F₃
- F₁ is greater than F₂, which is greater than F₃
Correct answer: F₁ is greater than F₂, which is greater than F₃
Solution
The forces on q₁ and q₂ are due to the charges they induce on the inner walls of the cavities, which are equal in magnitude but opposite in direction. The force on q₃ is weaker because it is at a large distance and experiences the net field of the entire conductor, which is smaller.
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