Two points charges q1=q2=2  μC are fixed at x1=+3  m  and  x2=−3  m as shown. A third particle of mass 1 g and charge q3=−4  μC is released from rest at y = 4 m. Find the speed (in terms of the nearest integer in ms−1) of the particle as it reaches the origin.

Here the charge q3 is attracted toward q1  and  q2  both, so the net force on q3 is toward the origin. As only force acting is conservative, we can use conservation of  mechanical energy. Let v be the speed of particle at origin. From energy of conservation principle, we getUi+Ki=U+Kor 14πε0[q3q2(r32)i+q3q1(r31)i+q2q1(r21)i]+0=14πε0[q3q2(r32)f+q3q1(r31)f+q2q1(r21)f]+12mv2Here, (r21)i=(r21)f. Substituting the proper values, 9×109[(−4)(2)5+(−4)(2)5]×10−12=9×109[(−4)(2)3+(−4)(2)3]×10−12+12×10−3  v2or (9×10−3)(−165)=(9×10−3)(−163)+12×10−3  v2or 9×10−3(16)(215)=12×10−3  v2or v=6.2  =6  ms−1