How to Calculate Electrostatic Potential

Electrostatic potential calculations are relevant in designing and maintaining power lines.

Electrostatic potential is important in understanding physical systems. Calculating electrostatic potential requires multiplication, exponent manipulation and "reading" unit prefixes. The most basic calculation of electrostatic potential is that for a single point charge.

Things You'll Need

• Calculator with arbitrary exponent (y^x) operation
• Integral solving software or table of trigonometric substitutions and integration schemes
• Textbook or reference covering electromagnetic physics

Instructions

1. Define electrostatic potential with respect to the given problem. Electrostatic potential is measured in volts -- work per unit charge -- required to move a charge a certain distance when it experiences an electric force due to other charges(s). Voltage units are J/C, with J corresponding to joules (energy) and C corresponding to coulombs (charge). To check on progress, keep units organized and coherent. Voltages of 5 coulombs or electrostatic potential measuring 16m are red flags that something is wrong in the calculation.

2. Use the formula V1 = k*q1/d1 for a particle with charge q1 that has electrostatic potential V1 at distance d1, where k is a constant equal to 8.987e9 J*m / C^2. Electric potential energy between two particles with charges q1 and q2 is U(1,2) = q2*V1 = k*q2*q1 / d, where d is distance between the two points.

3. Calculate V(a) = k*q(a) / d to find electrostatic potential 5 nanometers (5 nm) away. Consider particle with a charge of 4e, where e is the elementary charge, so e = 1.602E--19 coulombs (C).

4. Standardize units. Since 4e = 4*1.602e-19 = 6.408e-19 C. Distance of 5 nm = 5e-9 meters (5e-9 m). Therefore, V(a) = 8.987e9 * 6.408e-19 / (5e-9). The calculation shows that V(a) = 1.152 volts.

5. Check unit consistency. Electrostatic potential has units J/C. The expression "k * q(a) / d" has units [J*m / C^2] * [C / m]. The meter (m) units cancel, giving (J * C / C^2). One of the denominator (bottom) "C" terms cancel with the "C" in the numerator (top) of the fraction, leaving J / C. This matches voltage (V) units, as expected.

Tips & Warnings

• For the purposes of this article, parenthetical notation in variables does not mean multiplication. For instance, electrostatic potential is denoted by V and a given particle may be labeled as "a." Normally, an expression like V(a) would mean "V multiplied by a", just as 3(4) = 3*4 = 12. However, here, notation such as V(a) or U(a,b) means "electrostatic potential V of particle a" and "potential energy U of particles 'a' and 'b'."

• Units such as nanometers or picometers use prefixes indicating a numbered exponent. "Nano" corresponds to 10^-9 (one-billionth) and "pico" corresponding to 10^-12 (one-trillionth). For example, three nanometers correspond to 3*(10^-9), or equivalently, 3e-9 meters. UNC's "Metric Units" details metric prefixes and their corresponding exponents.

References

• University of North Carolina at Chapel Hill (UNC): Metric Prefixes
• University of New South Wales: Electrostatic Potential Energy
• University of Rochester: The Electrostatic Potential
• Department of Mathematics, California State University at Fullerton: Two-Dimensional Electrostatics
• Georgia State University: Equipotential Lines
• Worcester Polytechnic Institute: Indefinite Integration

Resources

• University of California at Davis: Integration of Trigonometric Integrals
• National University of Singapore: Lecture Notes on Advanced Calculus II
• Homework Help From Cramster: Electrostatic Potential