B

Step 1: Understand the function of the control grid in an electron gun. The control grid is a component that influences the flow of electrons emitted from the cathode.
Step 2: Recognize that applying a negative potential to the control grid relative to the cathode serves to create an electric field. This field can repel negatively charged electrons, which allows for better control over their flow.
Step 3: This repulsion can effectively regulate the number of electrons that pass through to the anode or to the next stage of the system.
Step 4: Therefore, the primary purpose of the negative potential at the control grid is to manage the number of electrons by repelling those that are not needed.
Therefore, the correct answer is Option B: Repel electrons and thus to control the number of electrons passing through it.