Potential Difference Between Two Parallel Charged Plates
Simple Explanation
Between two parallel plates carrying opposite charges, the electric field is uniform (constant strength and direction), and the potential difference between the plates is simply the field strength multiplied by the separation between them.
Why Do We Need It?
This relationship is the basis for how capacitors work, and provides a simple, precisely-controlled way to create a known, uniform electric field in the lab.
Formula
Potential Difference Between Parallel Plates
V = Ed
For a uniform electric field between two parallel charged plates, the potential difference between them equals the field strength multiplied by the separation between the plates.
- V
- — Potential difference between the plates, in volts
- E
- — Electric field strength between the plates, in V/m (uniform)
- d
- — Distance (separation) between the plates, in metres
When to use it: Use to find the potential difference across parallel plates given the field strength and separation, or to find the field strength given a known applied voltage.
Worked Example
Finding the field strength between plates
Two parallel plates are 0.02 m apart with a potential difference of 240 V between them. Find the electric field strength.
Why Does This Work?
Because the field between parallel plates is uniform (unlike the field around a point charge), the relationship between potential difference and distance is a simple direct proportion (rather than the inverse relationship seen for a point charge) — the field strength is constant everywhere between the plates, so V = Ed applies exactly at any point along the gap.
Real-Life Example
A cathode ray tube's deflection plates
Older television and oscilloscope cathode ray tubes use parallel plates to deflect a beam of electrons.
By applying a controlled potential difference across parallel deflection plates, engineers create a precisely known, uniform electric field that predictably steers the electron beam — directly using this relationship between voltage, field strength, and plate separation.
Practice
Two parallel plates 0.05 m apart have an electric field strength of 4000 V/m between them. Find the potential difference.
MediumCommon mistake
Applying V = kQ/r (the point-charge potential formula) to a parallel-plate setup — the field between parallel plates is UNIFORM, not radiating from a point, so the much simpler V = Ed relationship applies instead.
Quick Review
- V = Ed relates potential difference, field strength, and plate separation for a uniform field.
- The field between charged parallel plates is uniform, unlike the field around a point charge.
- This relationship underlies capacitors and devices like CRT deflection plates.