Electric Field Lines and Charge Magnitude Relationship

Based on the provided electric field lines diagram:

1. Sign and Magnitude of Charges:

   • The electric field lines originate from charge $Q_1$ and terminate on charge $Q_2$. This implies that $Q_1$ is a positive charge and $Q_2$ is a negative charge.
   • The number of electric field lines originating from or terminating on a charge is directly proportional to the magnitude of that charge ($N \propto |Q|$).
   • In the figure, a larger number of field lines originate from $Q_1$ than the number of lines terminating on $Q_2$ (several lines from $Q_1$ extend out to infinity). Therefore:
     $|Q_1| > |Q_2|$
   • Hence, Option (A) is correct and Option (B) is incorrect.

2. Location of the Neutral Point ($E = 0$):

   • The charges have opposite signs, so their electric fields between them point in the same direction (from the positive charge $Q_1$ towards the negative charge $Q_2$). Consequently, the electric field cannot be zero between the two charges.
   • Outside the charges along the line joining them, the fields due to $Q_1$ and $Q_2$ point in opposite directions. The net electric field can be zero where the magnitudes of the two fields are equal:
     $E = \frac{1}{4\pi\varepsilon_0}\frac{|Q_1|}{r_1^2} = \frac{1}{4\pi\varepsilon_0}\frac{|Q_2|}{r_2^2} \implies \frac{r_1}{r_2} = \sqrt{\frac{|Q_1|}{|Q_2|}}$
   • Since $|Q_1| > |Q_2|$, we must have $r_1 > r_2$ for the fields to cancel each other out.
   • For points to the left of $Q_1$, any point is closer to $Q_1$ than to $Q_2$ ($r_1 < r_2$). Because $|Q_1| > |Q_2|$ and $r_1 < r_2$, the field due to $Q_1$ is strictly greater than that due to $Q_2$ at all points to the left of $Q_1$, meaning the field can never be zero there. Thus, Option (C) is incorrect.
   • For points to the right of $Q_2$, any point is closer to $Q_2$ than to $Q_1$ ($r_2 < r_1$). Thus, the condition $r_1 > r_2$ is satisfied, and there exists a finite distance to the right of $Q_2$ where the two opposing electric fields cancel each other completely. Hence, Option (D) is correct.

Correct Options: A and D