Animated Solution for Physics - Electrostatics: A few electric field lines for a system of two charges $Q_1$ and $Q_2$ fixed at two different points on the x-axis are shown in the figure. These lines suggest that

When we look at the electric field lines for the system of two charges, $Q_1$ and $Q_2$, the first thing we notice is the direction of the arrows. The lines originate from $Q_1$ and terminate at $Q_2$.

By convention, electric field lines always start from positive charges and end on negative charges. This immediately tells us that $Q_1$ is a positive charge and $Q_2$ is a negative charge.

Now, let's talk about the magnitude of these charges. A fundamental property of electric field lines is that the number of lines originating or terminating at a charge is directly proportional to the magnitude of that charge.

If we carefully observe the diagram, we can see that there are more lines leaving $Q_1$ than there are entering $Q_2$. Some of the lines from $Q_1$ go off to infinity and never reach $Q_2$. This visual cue is a direct mathematical statement: the magnitude of $Q_1$ is strictly greater than the magnitude of $Q_2$.

This confirms that option (a) is correct.

Next, we need to find the neutral point—the location where the net electric field is exactly zero.

Because the charges have opposite signs, the electric fields they produce in the region between them will point in the same direction (away from the positive $Q_1$ and towards the negative $Q_2$). Therefore, they can never cancel each other out in this middle region. The neutral point must lie outside, on the line joining the two charges.

At the neutral point, the electric field due to $Q_1$ must perfectly balance the electric field due to $Q_2$:

Using the formula for the electric field of a point charge, we get:

Since we already established that $|Q_1|>|Q_2|$, the only way for this equation to hold true is if $r_1>r_2$. This means the neutral point must be further away from $Q_1$ and closer to $Q_2$.

Because $Q_2$ is on the right side of the setup, the neutral point must lie at a finite distance to the right of $Q_2$. This confirms that option (d) is also correct.