Step 1: The magnetic field at a point due to a current-carrying conductor is given by Ampere's Law, which states that the magnetic field is directly proportional to the current \( I \) flowing through the conductor.
Step 2: Therefore, the correct option is the current flowing through the conductor, as it is the factor that affects the magnetic field produced around the conductor.
Final Answer:
\[
\boxed{\text{current flowing through the conductor}}
\]