For a positive point charge q, what is the potential at infinity?

For a positive point charge q, what is the potential at infinity?

• A. ∞
• B. k q / r
• C. 0
• D. -k q / r

Answer: (C)

The main idea is that the electric potential from a point charge scales as 1/r and we choose infinity as the reference point where the potential is defined to be zero. For a positive charge, the potential at a distance r is V(r) = k q / r. Taking the limit as r becomes infinitely large, V(r) approaches zero. Since we set the potential to zero at infinity for isolated charges, the potential there is zero. The other options don’t fit: infinity would imply an unbounded potential, which isn’t the case for a finite charge; k q / r is the potential at a finite distance, not at infinity; and a negative sign would imply a negative potential, which doesn’t occur for a positive charge as you go to infinity—the potential approaches zero from the positive side.

The main idea is that the electric potential from a point charge scales as 1/r and we choose infinity as the reference point where the potential is defined to be zero. For a positive charge, the potential at a distance r is V(r) = k q / r. Taking the limit as r becomes infinitely large, V(r) approaches zero. Since we set the potential to zero at infinity for isolated charges, the potential there is zero.

The other options don’t fit: infinity would imply an unbounded potential, which isn’t the case for a finite charge; k q / r is the potential at a finite distance, not at infinity; and a negative sign would imply a negative potential, which doesn’t occur for a positive charge as you go to infinity—the potential approaches zero from the positive side.