A Calculate The Electric Potential 0.280 Cm From An Electron

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 infinity. The potential decreases as you move away from the electron.

This calculator helps you determine the electric potential at a distance of 0.280 cm from an electron. The calculation is based on Coulomb's Law, which describes the electrostatic force between two charged particles.

Formula

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

Where:

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

Example Calculation

Let's calculate the electric potential at a distance of 0.280 cm from an electron.

1. Convert the distance to meters: \( 0.280 \, \text{cm} = 0.00280 \, \text{m} \)
2. Use the formula: \( V = k \frac{q}{r} \)
3. Plug in the values:
   \( V = (8.9875 \times 10^9) \frac{-1.6022 \times 10^{-19}}{0.00280} \)
4. Calculate the result: \( V \approx -8.98 \, \text{V} \)

The electric potential at 0.280 cm from an electron is approximately -8.98 volts.

Interpreting Results

The negative sign indicates that the potential is negative relative to infinity. This means that work would be required to move a positive charge from infinity to this point.

The magnitude of the potential decreases as the distance from the electron increases. For example, doubling the distance would halve the potential.

This calculation is useful in understanding the behavior of charged particles in electric fields and is fundamental in many areas of physics and engineering.