In general, when is the electric field zero?

• A. Only at infinity
• B. Only if there are no charges
• C. Always zero at all points
• D. At points where the vector sum of the fields from all charges equals zero

Answer: (D)

Electric field at a point is the vector sum of the fields produced by every charge there. It can be zero when the contributions from all charges cancel each other exactly, so the net field points to zero. This means the condition for zero field is that the vector sum of all individual fields equals zero.

That includes the intuitive case that far away from all charges the field tends to zero, but more generally there can be finite locations where cancelation occurs depending on how the charges are arranged. So the general statement is: the electric field is zero at points where the vector sum of the fields from all charges equals zero.