Dipole Calculator

Enter the charge magnitude and separation distance to find the electric dipole moment (p = q × d), then compute the torque (τ = pE sin θ) and potential energy (U = −pE cos θ) of that dipole in a uniform external electric field.

Quick Facts

Dipole moment
p = q × d
Charge magnitude times separation distance; SI unit is the coulomb-meter (C·m).
Torque in a field
τ = pE sin θ
Maximum at θ = 90°, zero when p is aligned or anti-aligned with E.
Potential energy
U = −pE cos θ
Minimum (most stable) when p points along E; maximum when p opposes E.
Debye unit
1 D ≈ 3.336 × 10⁻³⁰ C·m
Common unit for reporting molecular dipole moments.

Your Results

Calculated
Electric Dipole Moment
-
p = q × d, in C·m (and Debye)
Torque on Dipole
-
τ = pE sin θ
Potential Energy
-
U = −pE cos θ
Maximum Possible Torque
-
τ_max = pE, occurs at θ = 90°

Ready

Enter charge, separation distance, field strength, and angle, then press Calculate.

Formula and Method for the Electric Dipole Calculator

An electric dipole is a pair of charges of equal magnitude and opposite sign, +q and −q, held a fixed distance d apart. The strength and orientation of that charge pair is captured by a single vector quantity, the electric dipole moment p = q × d, which points from the negative charge toward the positive charge. This calculator first finds the dipole moment from your charge and separation, then places that dipole in a uniform external electric field E and finds the torque and potential energy at the angle θ between the dipole moment and the field.

How the calculation works

Enter the charge magnitude q and separation distance d (with their units) to get the dipole moment, p = q × d, in coulomb-meters. Enter an external field strength E and the angle θ between the dipole moment vector and the field vector to get the torque the field exerts on the dipole, τ = pE sin θ, and the dipole's potential energy in that field, U = −pE cos θ. The calculator also reports the maximum possible torque, τ_max = pE, which occurs at θ = 90° regardless of the field strength.

Common mistakes

  • Mixing up torque and energy: torque uses sin θ and peaks at 90°; potential energy uses −cos θ and is most negative at 0°. They are not interchangeable.
  • Forgetting unit conversions: convert charge to coulombs and distance to meters before multiplying — a value entered in μC or cm must use the matching unit selector, not be typed as if it were already in C or m.
  • Working in degrees instead of radians: τ = pE sin θ and U = −pE cos θ assume θ is an angle measured consistently; if you compute by hand or in a spreadsheet that expects radians, convert first (radians = degrees × π/180).

Real-world applications

  • Chemistry uses molecular dipole moments (often reported in debyes) to predict polarity, solubility, and hydrogen bonding — water's dipole moment of about 1.85 D explains many of its solvent properties.
  • Dielectric materials inside capacitors polarize into countless tiny dipoles that align with an applied field, which is how dielectrics increase capacitance.
  • Dipole antennas radiate and receive electromagnetic waves based on an oscillating electric dipole moment driven by an alternating current.
  • Microwave ovens heat food by rapidly flipping an electric field to torque polar water molecules back and forth, converting that rotational motion into heat.

Frequently Asked Questions

What is an electric dipole moment?
An electric dipole is a pair of equal and opposite charges, +q and −q, separated by a small distance d. Its dipole moment is p = q × d, a vector pointing from the negative charge to the positive charge, with SI unit coulomb-meter (C·m). It measures how strongly the charge pair responds to, and generates, electric fields.
How do you calculate the torque on a dipole in an electric field?
Torque is τ = pE sin θ, where p is the dipole moment, E is the electric field strength, and θ is the angle between the dipole moment and the field. Torque is zero when the dipole is aligned or anti-aligned with the field (θ = 0° or 180°) and reaches its maximum, τ = pE, when the dipole is perpendicular to the field (θ = 90°).
What does the potential energy of a dipole mean, and why can it be negative?
The potential energy is U = −pE cos θ. It is most negative — the most stable orientation — when the dipole points along the field (θ = 0°), and most positive — the least stable — when it points opposite the field (θ = 180°). The negative sign shows that the field does positive work as the dipole rotates toward alignment.
What is a debye, and how does it relate to coulomb-meters?
The debye (D) is a common non-SI unit for molecular dipole moments, where 1 D ≈ 3.336 × 10⁻³⁰ C·m. It avoids the extremely small exponents that C·m produces at the molecular scale — for example, a water molecule has a dipole moment of about 1.85 D, or roughly 6.17 × 10⁻³⁰ C·m.

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