1. What is the Electric Potential to Field Equation?

The relationship between electric potential (V) and electric field (E) is given by the negative gradient of the potential. In one dimension, this simplifies to E = -dV/dr, where V is the electric potential and r is the distance.

2. How Does the Calculator Work?

The calculator uses the simplified equation:

Where:

• \( E \) — Electric field (V/m)
• \( \Delta V \) — Potential difference (V)
• \( \Delta r \) — Distance between points (m)

Explanation: The electric field is the negative of the rate of change of electric potential with respect to distance.

3. Importance of Electric Field Calculation

Details: Calculating electric fields from potential is fundamental in electromagnetism, helping design electrical systems, understand charged particle motion, and analyze electronic circuits.

4. Using the Calculator

Tips: Enter the potential difference in volts and the distance in meters. The distance must be greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: Why is there a negative sign in the equation?
A: The negative sign indicates that the electric field points in the direction of decreasing potential.

Q2: What are typical electric field values?
A: Near power lines might be 1-10 kV/m, while inside household wiring is much less. Breakdown field in air is about 3 MV/m.

Q3: When is this simplified equation valid?
A: For uniform electric fields or small distances where the field can be considered constant.

Q4: What are the limitations of this calculation?
A: For non-uniform fields, a more complete gradient calculation is needed. Also doesn't account for time-varying fields.

Q5: How does this relate to Coulomb's Law?
A: The electric field can also be calculated from point charges using Coulomb's Law, which is consistent with this potential-based approach.