Answer
(a) positive
(b) $5\mu C $
(c) $5\mu C $
Work Step by Step
(a) We know that the electric field lines begin at $ q_1$, $ q_3$ and end at $ q_2$. The electric field lines start at infinity or at a positive charge and end at a negative charge or at infinity. Thus, the charge at $ q_2$ is negative while $ q_2$ and $ q_3$ are positive.
(b) The number of lines entering and leaving a charge is proportional to the magnitude of the charge. We know that the magnitude of $ q_1$ is half of that of $ q_2$ and also of the opposite sign. Thus, $ q_1=\frac{10\mu C}{2}=5\mu C $
(c) We know that for the same reason as discussed in part(b), the magnitude of charge $ q_3=5\mu C $.
