Calculate the Force
Use SI units. The active model determines which values control the result.
Formula Used
Permanent dipole: F = p(dE/dx) cos(theta)
Induced dipole: F = alpha E(dE/dx) = 1/2 alpha d(E²)/dx
Dielectrophoretic sphere: F = 2π εm r³ Re[K] ∇(E_RMS²)
The permanent model uses a fixed dipole. The induced model assumes linear polarizability. The sphere model estimates dielectrophoresis in a dielectric medium. For a one-dimensional field, ∇(E²) becomes 2E(dE/dx).
How to Use This Calculator
- Select the model that matches the object and its environment.
- Enter electric field strength and the local field gradient in SI units.
- Fill the model-specific values, such as dipole moment, polarizability, or particle radius.
- Set a signed gradient to define the direction along your selected axis.
- Press Calculate Force. Review the signed result and its magnitude.
- Use the export buttons to save the calculated values as CSV or PDF.
Example Data Table
| Model | Key inputs | Force estimate | Interpretation |
|---|---|---|---|
| Permanent dipole | p = 1.0e−12 C·m; dE/dx = 1.0e8 V/m²; theta = 0° | 1.0e−4 N | Points along the positive gradient. |
| Induced dipole | alpha = 1.0e−24 C·m²/V; E = 1.0e5 V/m; dE/dx = 1.0e8 V/m² | 1.0e−11 N | Pulls toward stronger fields for positive alpha. |
| Dielectrophoretic sphere | r = 5.0e−6 m; εr = 80; Re[K] = 0.5 | About 5.6e−12 N | Uses ERMS and its squared-field gradient. |
Understanding Force on Polarized Objects
Field Behavior
A polarized object contains positive and negative charge that has shifted apart. Its total charge may still be zero. An external electric field can turn the object. That turning effect is torque. A changing field can also move the object. The movement becomes noticeable when one side experiences a stronger field than the other side of the same object does.
Field Gradient Matters
Field gradient describes how electric field strength changes with position. It is essential for predicting translation of neutral polarized objects. A larger gradient often produces a larger force. A perfectly uniform field may rotate a dipole. It normally gives no net push along one direction. This difference matters when designing sensors, separators, and small fluid handling devices for research teams.
Permanent Dipoles
Some objects have a permanent dipole moment. Their internal charge separation exists before the applied field arrives. Electrets and molecular systems can show this behavior. The force depends on dipole strength, field gradient, and orientation. Alignment with the field gives the largest positive component. A reversed alignment can change the sign. The result then points opposite the selected positive axis.
Induced Polarization
Many materials acquire polarization only after entering an electric field. Their dipole moment then depends on field strength. A linear response uses polarizability to connect these quantities. The energy stored by polarization changes when the field changes across space. This energy change creates force. The model works best for small isotropic objects whose material response remains proportional to the field.
Dielectrophoretic Spheres
Small dielectric spheres suspended in a liquid can experience dielectrophoresis. This effect is common in particle sorting equipment. The sphere model combines medium permittivity, particle radius, and a material contrast factor. Positive contrast pulls a particle toward stronger fields. Negative contrast pushes it away. Use root mean square values for alternating signals. Keep the field convention consistent throughout the calculation.
Units and Direction
Always use units consistently. Enter field strength in volts per meter. Enter the field gradient in volts per meter squared. Enter permanent dipole moment in coulomb meters. Enter polarizability in coulomb meter squared per volt. Enter radius in meters. The calculator reports force in newtons. A signed value gives direction. The absolute value gives magnitude. Recheck units before accepting results.
Practical Assumptions
The calculation uses a one dimensional field gradient. It does not replace a complete electromagnetic simulation. Electrodes can create curved fields. Large objects may change field around them. Conductive materials, nonlinear behavior, and frequency dependence can require a different approach. Check temperature, medium properties, electrode geometry, and object size. Use a more detailed model before making design or safety decisions.
Better Measurements
Measure the field profile near the object position. Estimate the gradient from a validated field map. Central differences can improve a local estimate. Record uncertainty in polarizability, radius, permittivity, and field measurements. Repeat calculations using upper and lower values. This shows sensitivity. It reveals dominant uncertainty sources. Compare models when appropriate. Select the model that matches the object and conditions.
Frequently Asked Questions
1. What is a polarized object?
A polarized object has separated positive and negative charge. The net charge can be zero. An external field can rotate it. A nonuniform field can also move it.
2. Why is a field gradient necessary?
A uniform field produces torque on an aligned dipole. It normally produces no net translational force. A field gradient is required for the simple force models used here.
3. When should I use the permanent dipole model?
Use permanent dipole when the object has a known fixed dipole moment. Examples include electrets and certain molecular systems. Use a signed gradient for direction.
4. When should I use the induced dipole model?
Use induced dipole for a small linear object whose dipole moment follows p = alpha E. This approximation assumes scalar polarizability and a slowly varying field.
5. When is the sphere model appropriate?
Choose spherical dielectrophoresis for a dielectric sphere in a medium. Enter RMS field values for alternating fields. Supply the real Clausius-Mossotti factor.
6. Which units should I enter?
Enter E in V/m. Enter dE/dx in V/m². Enter p in C·m, alpha in C·m²/V, radius in m, and force is returned in N.
7. What does a negative force mean?
A negative result points opposite to your chosen positive axis. Check the gradient sign, dipole orientation, and Clausius-Mossotti factor before interpreting direction.
8. How does the angle affect force?
The angle is used by the permanent-dipole model. It projects the dipole onto the field direction. Zero degrees gives the largest positive aligned component.
9. Does this replace numerical simulation?
No. The calculator uses local one-dimensional approximations. Complex electrode shapes, large particles, nonlinear media, and conductive objects may require numerical field simulation.
10. Can I use alternating electric fields?
For induced and sphere models, use RMS field quantities when your formulation calls for them. Keep field and gradient conventions consistent. Do not mix peak values with RMS values.
11. How can I assess uncertainty?
Repeat the calculation with high and low input estimates. Compare the range. Force can change strongly with radius, gradient, and polarizability.
Careful inputs produce trustworthy force estimates for practical physics.