2322014.00.4qqqqFxLε⎛⎞−=+⎜⎟⎝⎠πThe signs are chosen so that a negative force value would cause qto move leftward. We require Fq= 0 and solve for q3: 23324440.44499qqxqqLq=−⇒=− =−where x= L/3 is used. Note that we may easily verify that the force on 4.00qalso vanishes: ()2220422220009440494qqqqqqFLLLLLLxεε−=−πππ. 19. (a) If the system of three charges is to be in equilibrium, the force on each charge must be zero. The third charge q3must lie between the other two or else the forces acting on it due to the other charges would be in the same direction and q3could not be in equilibrium. Suppose q3is at a distance xfrom q, and L– xfrom 4.00q. The force acting
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