A Calculate The Electric Potential 0.380 Cm From An Electron

Introduction

The electric potential at a point in space is the 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 because work is required to bring a positive charge closer to the electron.

This calculation is important in understanding atomic and molecular structures, as well as in designing electronic devices. The electric potential around an electron decreases with distance, following an inverse square law.

Formula

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

Where:

• \( V \) is the electric potential (in volts, V)
• \( k \) is Coulomb's constant (\( 8.9875 \times 10^9 \, \text{N m}^2/\text{C}^2 \))
• \( q \) is the charge of the electron (\( -1.6022 \times 10^{-19} \, \text{C} \))
• \( r \) is the distance from the electron (in meters, m)

For the specific case of calculating the potential 0.380 cm from an electron, we'll use these standard values.

Worked Example

Let's calculate the electric potential at 0.380 cm from an electron.

1. Convert the distance to meters: \( 0.380 \, \text{cm} = 0.00380 \, \text{m} \)
2. Use the formula: \( V = k \frac{q}{r} \)
3. Plug in the values:
   \( V = (8.9875 \times 10^9) \frac{-1.6022 \times 10^{-19}}{0.00380} \)
4. Calculate the result:
   \( V \approx -6.99 \times 10^{-10} \, \text{V} \)

The negative sign indicates that work is required to bring a positive charge closer to the electron. The very small magnitude reflects how weak the electric force is at this distance.

Interpreting Results

The result shows that the electric potential at 0.380 cm from an electron is approximately -6.99 × 10⁻¹⁰ volts. This means:

• The potential is negative because the electron has a negative charge
• The value is extremely small, indicating the potential drops off rapidly with distance
• This potential is typical for atomic-scale distances