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Question

A charge Q located at a point r is in equilibrium under the combined electric field of three charges q1,q2,q3. If the charges q1,q2 are located at points r1 and r2 respectively, find the direction of the force on Q, due to q3 in terms of q1,q2,r1r2 and r.

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Solution

F1+F2+F3=0

14πϵ0Qq1|rr1|3(rr1)+14πϵ0Qq2|rr2|3(rr2)+14πϵ0Qq3|rr3|3(rr3)=0

q1|rr1|3(rr1)+q2|rr2|3(rr2)=q3|rr3|3(rr3)

rr3=|rr3|3q3[q1(rr1)|rr1|3+q2(rr2)|rr2|3]

Direction of force on Q due to q3 along (rr3) is given by

F3 = KQ[q1|rr1|3(r1r)+q2|rr2|3(r2r)].

1447365_1364611_ans_839f9b37e5dc47c5b5e25ca79d0a8d88.png

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