A Calculate The Electric Potential 0.390 Cm From An Electron

Calculating the electric potential at a specific distance from an electron is a fundamental physics problem that helps understand electrostatic interactions. This guide explains how to compute the potential using Coulomb's Law, provides a step-by-step example, and offers interpretation guidance.

Introduction

The electric potential at a point in space is the amount of work needed to move a unit positive charge from infinity to that point. For an electron, which has a negative charge, the potential is negative when measured from a positive test charge.

Coulomb's Law provides the foundation for calculating electric potential. The key parameters are:

Charge of the electron (q)
Distance from the electron (r)
Permittivity of free space (ε₀)

This calculator uses these parameters to compute the electric potential at any given distance from an electron.

Formula

The electric potential (V) at a distance r from a point charge q is given by Coulomb's Law:

V = k·(q/r)

Where:

V = electric potential (volts)
k = Coulomb's constant (8.9875 × 10⁹ N·m²/C²)
q = charge of the electron (-1.6022 × 10⁻¹⁹ C)
r = distance from the electron (meters)

For the specific case of 0.390 cm from an electron:

r = 0.390 cm = 0.00390 m

V = (8.9875 × 10⁹)(-1.6022 × 10⁻¹⁹)/0.00390

Example Calculation

Let's calculate the electric potential 0.390 cm from an electron:

Convert distance to meters: 0.390 cm = 0.00390 m
Plug values into the formula:

V = (8.9875 × 10⁹)(-1.6022 × 10⁻¹⁹)/0.00390
Calculate the numerator:

8.9875 × 10⁹ × -1.6022 × 10⁻¹⁹ = -1.4422 × 10⁻⁹ J
Divide by distance:

-1.4422 × 10⁻⁹ / 0.00390 ≈ -3.7 × 10⁻⁶ J/C
Convert joules to volts (1 J/C = 1 V):

V ≈ -3.7 × 10⁻⁶ V

The electric potential is approximately -3.7 microvolts at 0.390 cm from an electron.

Interpreting Results

The negative sign indicates that the potential is lower than at infinity, which is expected for a negative charge. The very small magnitude (microvolts) shows that the potential changes very gradually with distance for an electron.

Key points to consider:

The potential becomes more negative as you get closer to the electron
The potential changes more rapidly when closer to the electron
For practical purposes, the potential at this distance is negligible

Note: This calculation assumes the electron is stationary and isolated. In real scenarios, the electron would be part of an atom or molecule with additional interactions.

FAQ

What units should I use for the distance?

The calculator uses meters, but you can input centimeters which will be automatically converted. For 0.390 cm, the conversion is straightforward: 0.390 cm = 0.00390 m.

Why is the potential negative?

The negative sign indicates that the electron has a negative charge. The potential is measured relative to a positive test charge, so negative charges produce negative potentials.

How does distance affect the potential?

The potential varies inversely with distance. Doubling the distance halves the potential magnitude, and halving the distance doubles the potential magnitude.