Electric field between parallel plates — dependence on geometry The electric field strength between two parallel plates is proportional to the applied potential difference and inversely proportional to which geometric parameter?

Introduction / Context:
Parallel-plate models are widely used to approximate fields in capacitors and sensors. For uniform fields (neglecting fringing), the field is controlled by voltage and spacing, which is critical for breakdown calculations and capacitance design.

Given Data / Assumptions:

• Two large, parallel conducting plates.
• Uniform field assumption (edge effects neglected).
• Applied potential difference V across separation d.

Concept / Approach:
The ideal relationship is E = V / d. Thus, for a given voltage, increasing the gap reduces the field, and decreasing the gap increases the field. Materials and permittivity affect capacitance but not the basic proportionality of E to V and 1/d in vacuum or uniform dielectrics.

Step-by-Step Solution:
Start with definition: E = potential difference / distance.Write: E = V / d.At constant V, E varies inversely with d; doubling d halves E, halving d doubles E.Therefore, the inverse geometric dependence is on the plate separation.

Verification / Alternative check:
Check units: V in volts, d in meters, so E has units of V/m, matching electric field units. Experimental setups also confirm breakdown thresholds scale with gap distance for similar conditions.

Why Other Options Are Wrong:

• Negative plate only: field depends on both plates and their potential difference, not one plate in isolation.
• Field strength: circular reasoning; we are explaining E, not expressing it in terms of itself.
• Charge difference: while related, in this geometry E is directly tied to V and d; charge adjusts to satisfy boundary conditions.

Common Pitfalls:

• Confusing field dependence (E = V/d) with capacitance dependence (C = εA/d).
• Neglecting fringing; in closely spaced small-area plates, non-uniformities can matter.

Final Answer:
plate separation