Electric Forces and Electric Fields1315.14Assume that the third bead has charge Qand is located at 0xd<<. Then the forces exerted on it by the +3qcharge and by the +1qcharge have magnitudes ( )323ekQqFx=and ( )()12ekQ qFdx=−respectively These forces are in opposite directions, so charge Qis in equilibrium if . This gives 3FF=1( )223x−=, and solving for x, the equilibrium position is seen to be 0.63411 3d==+This is a position of stable equilibrium if 0Q>. In that case, a small displacement from the equilibrium position produces a net force directed so as to move Qback toward the equilibrium position. 15.15Consider the free-body diagram of one of the spheres given
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