Three charges q1=3µC, q2=4µC and q3=7µC are placed on the circumference of a circle of radius 1 m . . .

Question : Three charges q₁=3µC, q₂=4µC and q₃=7µC are placed on the circumference of a circle of radius 1 m as shown. What is the value of charge q₄ placed on the same circle, if the potential at the centre, V₀=0? 

Doubt by Mohini

Solution :
According to superposition principle, 
Total Potential at the centre O will be given by 
V=V1+V2+V3+V4
V=(kq₁/r)+(kq₂/r)+(kq₃/r)+(kq₄/r)
V=k(q₁+q₂+q₃+q₄)/r
∵ V=0 (Given)
0=k(q₁+q₂+q₃+q₄)/r
(0×r)/k=q₁+q₂+q₃+q₄
0=3µC+4µC+7µC+q4
0=14µC+q4
q4=-14µC

Hence, the required value of q₄ will be -14µC.