Electric Dipole Calculator
Calculate dipole field and potential energy at distance r and angle θ
Parameters
Controls
Calculated Values
Examples
p = 10⁻⁹ C·m, r = 0.1 m
On-axis field estimate.
p = 2×10⁻⁹ C·m, θ = 60°
Energy in external field context.
Visualization
Electric Dipole — Field, Torque, and Energy
An electric dipole consists of +q and −q separated by distance d. Dipole moment p⃗ = q d⃗ points from − to +, SI unit C·m.
Far from the dipole (r >> d), field falls as 1/r³ (faster than point charge 1/r²). On axis: E ≈ 2kp/r³; on equatorial line: E ≈ kp/r³.
Torque in uniform field: τ⃗ = p⃗ × E⃗, magnitude τ = pE sinθ. Dipole tends to align with E (θ → 0 minimizes energy).
Potential energy U = −p⃗·E⃗ = −pE cosθ. Stable equilibrium at θ = 0 (aligned); unstable at θ = π.
Polar molecules (H₂O, HCl) have permanent p; nonpolar molecules can gain induced dipole in external E (polarization).
Dipole radiation: accelerating or oscillating dipoles emit EM waves — basis of antenna theory at λ >> dipole size.
Key Concepts
- p = qd — dipole moment
- E ∝ 1/r³ at large r
- τ = pE sinθ — torque
- U = −pE cosθ — potential energy
- Stable when p parallel to E
- Net charge zero, field nonzero
Real-World Applications
- Polar solvents and dielectrics
- Dipole antennas (radio/TV)
- Liquid crystal displays
- Molecular orientation in E fields
- Class 12 dipole field derivations
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Physics Equations
Step-by-Step Solution
See how the main results are calculated.
Step 1: Dipole Moment
Equation:
Result:
Explanation:
Vector from −q to +q, magnitude q×separation. Net charge of ideal dipole is zero.
Step 2: Geometry — Distance and Angle
Field point at distance r from center, angle θ from dipole axis.
Calculation:
Explanation:
Valid for r >> dipole size d (point dipole approximation).
Step 3: On-Axis Field Reference
Equation:
Calculation:
Explanation:
On-axis field is twice equatorial field at same r for ideal dipole.
Step 4: Field at Angle θ
Evaluate field magnitude at observation angle θ from dipole axis.
Calculation:
Result:
Explanation:
General point-dipole field components combine to this magnitude at angle θ.
Step 5: Potential Energy in External Field
Equation:
Calculation:
Result:
Explanation:
Minimum U at θ = 0° (aligned); maximum at θ = 180°; U = 0 at θ = 90°.
Step 6: Torque Tending to Align Dipole
Equation:
Calculation:
Explanation:
Torque rotates dipole until p aligns with E (stable equilibrium at θ = 0 in uniform field).
Frequently Asked Questions (FAQ)
Why 1/r³ for dipole?
At large r, +q and −q fields nearly cancel; leading term is dipole contribution ∝ p/r³.
Field on equatorial vs axial line?
Different geometry factors but both ∝ 1/r³; axial is 2× equatorial for same r (ideal point dipole).
Can a dipole feel force in uniform E?
Pure uniform E: torque only. Non-uniform E can exert net force (F ∝ ∇(p·E)).
Induced vs permanent dipole?
Permanent: fixed p. Induced: p from electron shift in external E (polarization).
Energy at θ = 90°?
U = 0 (cos 90° = 0) — neither max nor min; unstable equilibrium in 2D rotation.
Practice MCQs
- Stable equilibrium angle for dipole in uniform E:
- Compared to point charge field at large r, dipole field E falls as:
- Dipole moment p has units:
- Maximum torque on dipole in field E occurs at:
- Net charge of an ideal dipole is:
- Water is a good solvent partly because it is:
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