Calculate the Electric Potential 0.140 cm from an Electron
Use this interactive physics calculator to find electric potential using Coulomb’s law. Enter the distance, choose the charge type, and instantly see the potential in volts, the distance conversion in meters, and a chart showing how potential changes with distance.
Electric Potential Calculator
This calculator applies the equation V = kq/r, where k = 8.9875517923 × 109 N·m2/C2.
Default example: electric potential at 0.140 cm from an electron.
Potential vs Distance Chart
The plot below updates after each calculation. It compares how electric potential changes with distance for the selected charge magnitude.
How to Calculate the Electric Potential 0.140 cm from an Electron
Finding the electric potential at a point near a charged particle is a classic electrostatics problem. In this case, the question asks for the electric potential at a distance of 0.140 cm from an electron. Because an electron is a point charge with a known negative elementary charge, the solution comes directly from Coulomb’s law in potential form. This page gives you both a calculator and a complete conceptual explanation, so you can understand not only the answer, but also why the answer has the sign and magnitude it does.
Electric potential is a scalar quantity that describes the electric potential energy per unit charge at a point in space. For a point charge, the electric potential is determined by:
V = kq/r
where V is 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.
Step 1: Convert 0.140 cm into meters
The most common source of mistakes in electrostatics problems is unit conversion. Coulomb’s law uses SI units, so distance must be in meters. Since:
- 1 cm = 0.01 m
- 0.140 cm = 0.140 × 0.01 m
- 0.140 cm = 0.00140 m
This means the distance from the electron is 1.40 × 10-3 m.
Step 2: Use the electron’s charge
The charge of a single electron is an exact defined physical constant in the SI system:
- q = -1.602176634 × 10-19 C
The negative sign matters. Electric potential keeps the sign of the source charge. That means any point around an isolated electron has a negative electric potential relative to zero at infinity.
Step 3: Insert the values into the equation
Now substitute the known values into the point charge potential formula:
- k = 8.9875517923 × 109 N·m2/C2
- q = -1.602176634 × 10-19 C
- r = 1.40 × 10-3 m
So:
V = (8.9875517923 × 109)(-1.602176634 × 10-19) / (1.40 × 10-3)
Carrying out the multiplication in the numerator first gives approximately:
kq ≈ -1.440 × 10-9
Then divide by 1.40 × 10-3:
V ≈ -1.028 × 10-6 V
Therefore, the electric potential 0.140 cm from an electron is about -1.03 microvolts.
Why the result is negative
Students often ask why the answer is negative even though distance is always positive. The reason is simple: distance controls magnitude, while the sign comes from charge. Because an electron has negative charge, the potential it creates is negative everywhere in space, except at infinity where the reference is taken to be zero. If the same calculation were done for a proton at the same distance, the result would have the same magnitude but a positive sign.
| Source charge | Charge value | Distance | Electric potential |
|---|---|---|---|
| Electron | -1.602176634 × 10-19 C | 0.140 cm | -1.028 × 10-6 V |
| Proton | +1.602176634 × 10-19 C | 0.140 cm | +1.028 × 10-6 V |
Physical interpretation of electric potential
Electric potential tells you how much electric potential energy a positive test charge would have per coulomb at a particular point. A negative electric potential means that a positive test charge placed there would have negative electric potential energy relative to infinity. In plain language, the electron attracts a positive test charge, so the system’s potential energy decreases as the positive charge moves closer.
Since potential is a scalar, you do not need to worry about directional components the way you do with electric field vectors. That makes potential problems simpler in many cases. However, the sign remains physically meaningful because it tells you whether the source charge is positive or negative and whether a positive test charge would be attracted or repelled.
Why distance matters so much
The formula shows that electric potential is inversely proportional to distance. If you cut the distance in half, the magnitude of the potential doubles. If you increase the distance by a factor of ten, the magnitude decreases by a factor of ten. This is why the chart on this page changes steeply at small distances and flattens out as distance becomes larger.
For the specific question of 0.140 cm, the distance is actually quite large on the atomic scale. Atomic radii are typically around 10-10 m, while 0.140 cm is 1.40 × 10-3 m, many orders of magnitude farther away than typical atomic distances. That is one reason the potential magnitude here is only around a microvolt.
| Distance from an electron | Distance in meters | Approximate potential | Observation |
|---|---|---|---|
| 1 nm | 1.0 × 10-9 m | -1.44 V | Nanoscale distances produce much larger potential magnitudes. |
| 1 μm | 1.0 × 10-6 m | -1.44 × 10-3 V | Microscale distances reduce the potential by 1000 times compared with 1 nm. |
| 0.140 cm | 1.40 × 10-3 m | -1.028 × 10-6 V | The default problem sits in the microvolt range. |
| 1 cm | 1.0 × 10-2 m | -1.44 × 10-7 V | At larger macroscopic distances, the potential becomes very small. |
Common mistakes when solving this problem
- Forgetting to convert centimeters to meters. If you use 0.140 directly instead of 0.00140 m, your answer will be off by a factor of 100.
- Dropping the negative sign of the electron. The sign is essential because potential from a negative charge is negative.
- Confusing electric potential with electric field. Electric field uses E = kq/r2, while electric potential uses V = kq/r.
- Using the wrong reference point. In introductory physics, electric potential is generally taken as zero at infinity for isolated point charges.
Electric potential compared with electric field
It helps to distinguish these two related but different quantities:
- Electric potential, V, is scalar and measured in volts.
- Electric field, E, is vector and measured in newtons per coulomb or volts per meter.
- Potential tells you energy per unit charge, while field tells you force per unit charge.
- For a point charge, both depend on distance, but not in the same way.
If you were asked for the electric field 0.140 cm from an electron instead, the formula would involve 1/r2, which falls off much faster than potential. That is why potential often remains easier to work with over extended distances.
Where the constants come from
The elementary charge is one of the most important exact constants in modern SI. Since the 2019 SI redefinition, the value of the elementary charge is fixed exactly at 1.602176634 × 10-19 C. Coulomb’s constant is closely related to the vacuum permittivity and is approximately 8.9875517923 × 109 N·m2/C2. These constants are not arbitrary. They arise from the structure of electromagnetism and are supported by precise measurement standards.
Practical meaning of a microvolt scale answer
The result here is on the order of 10-6 volts, which is a microvolt. To put that in perspective, microvolt level signals matter in precision electronics, biomedical instrumentation, and low noise sensors. Although the isolated electron’s potential at this macroscopic distance is tiny, the same physics scales up when many charges are present. In circuits and materials, the collective effect of many electrons can produce measurable and technologically important voltages.
How this calculator helps
This calculator is built for both learning and verification. You can:
- Enter the exact problem distance of 0.140 cm.
- Switch between electron, proton, or custom charge.
- See the result in scientific notation and standard decimal formatting.
- Visualize how potential changes as distance increases.
- Check unit conversions automatically.
That makes it useful for homework, exam review, tutoring, or simply building intuition about inverse distance behavior in electrostatics.
Authoritative references for further study
If you want to confirm the constants and deepen your understanding, these sources are excellent starting points:
- NIST, elementary charge constant
- NASA Glenn Research Center, basics of electric charge and Coulomb interactions
- University level electric potential overview
Final answer for the stated problem
For an electron with charge -1.602176634 × 10-19 C at a distance of 0.140 cm = 0.00140 m, the electric potential is:
V ≈ -1.028 × 10-6 V
Rounded to three significant figures, this is -1.03 × 10-6 V.
Values shown here use Coulomb’s law for a point charge in vacuum. At an introductory physics level, this is the standard model for the problem.