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15. (a) There is no equilibrium position for q 3 between the two fixed charges, because it is being pulled by one and pushed by the other (since q 1 and q 2 have different signs); in this region this means the two force arrows on q 3 are in the same direction and cannot cancel. It should also be clear that off-axis (with the axis defined as that which passes through the two fixed charges) there are no equilibrium positions. On the semi-infinite region of the axis which is nearest q 2 and furthest from q 1 an equilibrium position for q 3 cannot be found because | q 1 | < | q 2 | and the magnitude of force exerted by q 2 is everywhere (in that region) stronger than that exerted by q 1 on q 3 . Thus, we must look in the semi-infinite
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