the three diagrams show electric field lines around a pair of like charges. which diagram shows a net force…

Explanation:

Step1: Recall force - field relationship

The force on a charge in an electric field is given by $\vec{F} = q\vec{E}$. A net force of zero means the electric field at point $X$ is zero.

Step2: Analyze electric - field line density

Electric - field lines represent the direction and magnitude of the electric field. The electric field is zero at a point where the electric - field lines from the two like charges cancel each other out. This occurs at the mid - point between two equal like charges. In the third diagram, point $X$ is at the mid - point between the two equal positive charges $q$. At this mid - point, the electric fields due to the two charges are equal in magnitude and opposite in direction, resulting in a net electric field of zero at point $X$.

Answer:

The third diagram.