In a uniform electric field, the magnitude of the field is related to potential difference and distance by E = ΔV/Δs. Which statement correctly expresses this relation for magnitudes?

• A. E = ΔV/Δs
• B. E = -ΔV/Δs
• C. E = Δs/ΔV
• D. E = -Δs/ΔV

Answer: (A)

The key idea is that the field strength is how fast the electric potential changes with distance. In one dimension, the signed relation is E = -dV/ds, meaning the field points in the direction of decreasing potential. When we talk about magnitudes, the sign is dropped, so the size of the field equals the change in potential per unit distance: |E| = |ΔV|/Δs. If you take ΔV as a potential difference regardless of sign (a positive quantity), you obtain E = ΔV/Δs for the magnitude. The minus sign is essential for the vector relation, but it disappears here because we’re focusing on the magnitude.