3.1. Suppose that the Faraday concentric sphere experiment is performed in free space using a central charge at the origin, Q₁, and with hemispheres of radius a. A second charge Q2 (this time a point charge) is located at distance R from Q1, where R >> a. a) What is the force on the point charge before the hemispheres are assembled around Q₁? This will be simply the force beween two point charges, or F = = aμ 4л€ R² b) What is the force on the point charge after the hemispheres are assembled but before they are discharged? The answer will be the same as in part a because induced charge Q₁ now resides as a surface charge layer on the sphere exterior. This produces the same electric field at the Q2 location as before, and so the force acting on Q2 is the same. c) What is the force on the point charge after the hemispheres are assembled and after they are discharged? Discharging the hemispheres (connecting them to ground) neutralizes the positive outside surface charge layer, thus zeroing the net field outside the sphere. The force on Q2 is now zero. d) Qualitatively, describe what happens as Q2 is moved toward the sphere assembly to the extent that the condition R >> a is no longer valid. Q2 itself begins to induce negative surface charge on the sphere. An attractive force thus begins to strengthen as the charge moves closer. The point charge field approximation used in parts a through c is no longer valid.