Electric Potential Calculator: 0.220 cm from an Electron
Use this premium calculator to compute the electric potential created by a point charge at a specific distance. It is preconfigured for the classic physics problem of finding the potential 0.220 cm from an electron, while still letting you change the charge type, distance, and units for comparison.
Interactive Calculator
Electric potential from a point charge is calculated with the equation V = kq/r, where k is Coulomb’s constant, q is the charge, and r is the distance from the charge.
Potential vs Distance Chart
The chart visualizes how electric potential changes with distance from the selected charge. For a point charge, the magnitude of the potential scales inversely with distance.
A negative charge such as an electron produces a negative electric potential. A positive charge such as a proton produces a positive electric potential.
How to Calculate the Electric Potential 0.220 cm from an Electron
Finding the electric potential at a given distance from an electron is a standard electrostatics problem, but it also offers a great opportunity to understand how point charges shape electric fields and potential energy. In this guide, we will walk through the exact physics, the unit conversion, the correct formula, the sign convention, and the numerical result for the specific question: What is the electric potential 0.220 cm from an electron?
The Core Idea Behind Electric Potential
Electric potential is a measure of electric potential energy per unit charge. In simple terms, it tells you how much energy a positive test charge would have, per coulomb, at a certain location in space due to another charge. The SI unit of electric potential is the volt, where one volt equals one joule per coulomb.
For a point charge, the electric potential is given by:
Here, V is the electric potential in volts, k is Coulomb’s constant, q is the source charge in coulombs, and r is the distance from the charge in meters. This equation assumes vacuum or air, which is how most textbook problems are framed unless otherwise stated.
Known Values for This Problem
To solve the problem, we identify the standard constants and the given distance:
- Charge of an electron: q = -1.602176634 × 10-19 C
- Coulomb’s constant: k = 8.9875517923 × 109 N·m²/C²
- Distance from the electron: 0.220 cm
The most common mistake in this problem is forgetting to convert centimeters to meters. Since the SI unit for distance in the equation is meters, we must convert 0.220 cm properly before plugging it into the formula.
Step 1: Convert 0.220 cm to Meters
There are 100 centimeters in 1 meter, so:
This can also be written in scientific notation as 2.20 × 10-3 m. Both forms are equivalent and valid for the calculation.
Step 2: Substitute Into the Electric Potential Formula
Now substitute the values into the equation:
Multiply the constants in the numerator first:
Then divide by the distance:
Rounded to three significant figures, the electric potential is:
Final Answer
The electric potential 0.220 cm from an electron is:
The negative sign matters. It tells you that the source charge is negative, so the electric potential it creates is also negative at every finite point relative to infinity.
Why the Potential Is Negative
In electrostatics, the sign of electric potential follows the sign of the source charge in the equation V = kq/r. Since an electron has negative charge, the potential produced by it is negative. If you replaced the electron with a proton, the same magnitude of charge would produce the same numerical value but positive instead of negative.
This is easy to see conceptually:
- A positive source charge creates positive electric potential.
- A negative source charge creates negative electric potential.
- The farther away you are, the smaller the magnitude of the potential.
Because the electron’s charge is extremely small, the voltage at a macroscopic distance like 0.220 cm is also very small in magnitude.
Comparison Table: Same Distance, Different Charges
The table below compares the electric potential at the same distance, 0.220 cm, for a few source charges. This helps show how both sign and charge magnitude matter.
| Source Charge | Charge Value (C) | Distance (m) | Electric Potential (V) | Interpretation |
|---|---|---|---|---|
| Electron | -1.602176634 × 10-19 | 2.20 × 10-3 | -6.55 × 10-7 | Negative because the source charge is negative |
| Proton | +1.602176634 × 10-19 | 2.20 × 10-3 | +6.55 × 10-7 | Same magnitude as the electron, opposite sign |
| 1 nC point charge | 1.00 × 10-9 | 2.20 × 10-3 | 4.09 × 103 | Much larger because the charge is enormously bigger than one elementary charge |
How Potential Changes with Distance
Electric potential from a point charge follows an inverse relationship with distance. If you double the distance, the potential becomes half as large in magnitude. If you cut the distance in half, the potential doubles in magnitude.
This inverse law is one reason physicists and engineers pay so much attention to scale. At atomic distances, a single electron can create significant local effects. At centimeter distances, the potential from a single elementary charge becomes very small.
| Distance from Electron | Distance in Meters | Electric Potential (V) | Relative to 0.220 cm Case |
|---|---|---|---|
| 0.110 cm | 1.10 × 10-3 | -1.31 × 10-6 | 2 times larger magnitude |
| 0.220 cm | 2.20 × 10-3 | -6.55 × 10-7 | Reference value |
| 0.440 cm | 4.40 × 10-3 | -3.27 × 10-7 | Half the magnitude |
| 1.00 cm | 1.00 × 10-2 | -1.44 × 10-7 | Much smaller magnitude |
Common Mistakes Students Make
- Not converting centimeters to meters. The formula uses SI units, so distance must be in meters.
- Dropping the negative sign. An electron has negative charge, so the potential must be negative.
- Using electric field instead of electric potential. These are related but different quantities. Electric field for a point charge is E = kq/r2, not kq/r.
- Confusing potential with potential energy. Potential is measured in volts, while potential energy is measured in joules.
- Using rounded constants too aggressively. In many educational settings, using k = 9.0 × 109 is acceptable, but for precision, the CODATA value is preferred.
Potential Versus Electric Field
Students often ask whether they should use electric field or electric potential when a problem mentions distance from a charge. The answer depends on what is being asked. If the problem asks for the force per unit charge at a point, that is the electric field. If the problem asks for energy per unit charge, that is the electric potential.
- Electric field: vector quantity, measured in N/C or V/m
- Electric potential: scalar quantity, measured in volts
- Potential energy: energy of a specific charge in the field, measured in joules
For the present question, because the wording asks for electric potential, the correct formula is definitely V = kq/r.
Why the Result Seems So Small
At first glance, many learners expect a huge voltage because Coulomb’s constant is large, roughly 8.99 × 109. However, the charge of one electron is extraordinarily tiny, only 1.602 × 10-19 C. When those values are multiplied, the result is still a very small number. At a distance of several millimeters or fractions of a centimeter, the resulting potential from a single electron is therefore only a tiny fraction of a volt.
In practical electronics, voltages usually come from astronomical numbers of electrons moving collectively, not from a single isolated electron at a macroscopic distance.
Useful Physical Constants and Reference Data
Below are several relevant constants often used in introductory physics and engineering calculations:
- Elementary charge: 1.602176634 × 10-19 C
- Coulomb constant: 8.9875517923 × 109 N·m²/C²
- Vacuum permittivity: 8.8541878128 × 10-12 F/m
- 1 centimeter: 1.00 × 10-2 m
These values are standardized and are available from authoritative scientific references. For students and professionals who want to verify the constants or study the broader theory of electrostatics, the following sources are excellent starting points:
Worked Example Summary
Here is the full process in concise form:
- Write the equation: V = kq/r
- Identify the charge of an electron: q = -1.602176634 × 10-19 C
- Convert the distance: 0.220 cm = 2.20 × 10-3 m
- Substitute: V = (8.9875517923 × 109)(-1.602176634 × 10-19)/(2.20 × 10-3)
- Calculate: V ≈ -6.55 × 10-7 V
If your result is positive, your sign is wrong. If your result is around -6.55 × 10-5 V or -6.55 × 10-9 V, your unit conversion is likely wrong.
When This Formula Applies
This equation applies when the source can be approximated as a point charge, or when you are outside a spherically symmetric charge distribution where the field acts like that of a point charge. It also assumes the reference of zero potential at infinity, which is the standard choice in electrostatics. In media other than vacuum or air, material properties can alter the effective interactions, but the textbook problem here clearly uses the ideal point-charge expression.
Bottom Line
To calculate the electric potential 0.220 cm from an electron, you use the point-charge potential equation, convert the distance to meters, and retain the negative sign of the electron’s charge. The correct result is:
This calculator automates the process and also lets you compare how the answer changes with other distances and source charges, helping you build deeper intuition about inverse relationships and sign conventions in electrostatics.