Calculator
Formula used
A velocity selector uses crossed electric and magnetic fields. For a charged particle moving straight through, the transverse forces cancel:
- FE = qE (electric)
- FB = qvB (magnetic, perpendicular motion)
Setting qE = qvB gives the pass speed: v = E/B. Rearrangements give E = vB and B = E/v.
How to use this calculator
- Select a mode: compute v, E, or B.
- Enter the known field and/or speed values with units.
- Click Calculate to show results above the form.
- Optionally, add v_test, d, q, and m for mismatch analysis.
- Use the export buttons to download CSV or PDF reports.
Example data table
| E (V/m) | B (T) | Pass speed v = E/B (m/s) | Region length d (m) | Sample v_test (m/s) |
|---|---|---|---|---|
| 2.5×104 | 0.20 | 1.25×105 | 0.08 | 1.20×105 |
| 1.0×105 | 0.50 | 2.00×105 | 0.10 | 2.05×105 |
| 8.0×103 | 0.10 | 8.00×104 | 0.05 | 7.80×104 |
These examples show how the pass speed scales linearly with E and inversely with B.
Velocity selector notes
1) What a velocity selector does
A velocity selector (often called a Wien filter) passes only particles whose speed matches a specific value. With electric and magnetic fields at right angles, slow and fast particles are pushed in opposite directions, while the “pass speed” travels straight down the centerline.
2) Crossed-field balance and pass speed
The electric force has magnitude qE. The magnetic force has magnitude qvB when motion is perpendicular to B. When the forces oppose and balance, the charge cancels and the selector becomes a speed filter with v = E/B. This is why the same selector can work for ions or electrons. For example, with E = 5.0×104 V/m and B = 0.50 T, the pass speed is v = 1.0×105 m/s in a straight beamline.
3) Practical field ranges
In laboratories, electric fields from about 103 to 106 V/m and magnetic fields from 10-3 to 1 T are common, depending on geometry. Larger E or smaller B increases the pass speed.
4) Acceptance bandwidth and beam quality
Real selectors have finite plate spacing, fringe fields, and beam divergence, so they transmit a band of speeds rather than a single value. Tightening slits, increasing interaction length, and improving field uniformity reduce the transmitted spread, but also reduce intensity.
5) Deflection, force, and energy view
If a particle enters with a test speed vtest, the net transverse force is F = q(E − vB). This calculator estimates acceleration a = F/m, then a small-angle deflection using y ≈ 0.5 a t2 with t = d/v. It helps connect field settings to measurable beam displacement.
6) Why selectors appear in mass spectrometers
Many mass spectrometers combine a selector with a magnetic analyzer. The selector first “standardizes” speed, so the analyzer’s bending radius depends mainly on m/q. This improves resolution and simplifies calibration.
7) Unit consistency and measurement uncertainty
Because v = E/B, a 2% uncertainty in E and 2% in B can produce roughly 4% uncertainty in v in worst cases. Using stable power supplies, calibrated probes, and consistent SI units improves repeatability.
8) Safe and realistic use
High voltages and strong magnets can be hazardous. Verify insulation, spacing, and interlocks, and avoid exceeding breakdown limits. For accurate design work, compare calculations against measured field maps and include fringe-field corrections when needed.
FAQs
1) Does the pass speed depend on charge?
No. In the ideal crossed-field balance, q cancels and v = E/B. Charge only affects force magnitude when the particle is off-speed.
2) What happens if the particle speed is higher than E/B?
The magnetic term qvB dominates, so the net force reverses direction compared with a slower particle. The beam deflects toward the side set by your field orientation.
3) Can a selector work for neutral particles?
No. Neutral particles have q = 0, so both electric and magnetic forces are zero. A selector requires charged particles to filter by speed.
4) Why do real devices transmit a range of speeds?
Finite plate spacing, non-uniform fields, and fringe regions mean the balance is imperfect across the aperture. Beam divergence and collisions also broaden the transmitted speed distribution.
5) Which mode should I use: solve for v, E, or B?
Use v when you set fields and want the pass speed. Use E or B when targeting a known speed and designing the required field strength.
6) What units should I enter for best results?
SI units are safest: E in V/m, B in tesla, and speeds in m/s. The calculator converts common alternatives, but consistent SI input reduces mistakes.
7) Is the deflection estimate always accurate?
It is a small-angle, uniform-field estimate. If fields vary strongly, speeds change inside the region, or deflections are large, use a more detailed trajectory model or measured field maps.