Beam-angle alignment study
With |q| = 1.6 microC, v = 5 km/s, and B = 250 mT, the envelope is 0.002 N and the 30-degree force is 0.001 N, exactly half maximum.
Physics and electromagnetism
Magnetic Force Graph Calculator
Generate an exact graph-ready table of magnetic-force magnitude versus angle from 0 to 180 degrees, including a selected reference angle and normalized force.
Graph-ready angular response
Tabulate the sine response behind magnetic force
This fifth-wave page intentionally provides a live exact angle-sweep table rather than a custom interactive chart. It isolates how |F| changes with the angle between velocity and B while holding charge magnitude, speed, and field constant.
Force at reference-
Maximum force-
Fraction of maximum-
Table point count-
Current model evidence
Magnetic-force angle sweep
Export the exact current table for plotting or interpolation; endpoints and symmetry provide the independent audit.
| Angle theta (deg) | sin(theta) | Force magnitude (N) | Fraction of maximum | Point type |
|---|
DETAILED CALCULATION PROCESS
Formula, units, default substitution, and reconciliation
1. Governing relation
|F(theta)| = |q| v B sin(theta), for 0 <= theta <= 180 deg
Convert the three scale inputs to SI, compute the envelope |q|vB, evaluate the selected angle, then enumerate every requested step from 0 to 180 degrees and insert the reference angle if it is off-grid.
2. Symbols and default basis
| Symbol | Meaning | Unit | Default basis |
|---|---|---|---|
| |q| | Charge magnitude | C | 1.6 microC |
| v | Particle speed | m/s | 5 km/s |
| B | Magnetic-field magnitude | T | 250 mT |
| theta | Angle between v and B | deg | 30 deg |
| Fmax | Perpendicular-force envelope |q|vB | N | Solved |
| F/Fmax | Normalized angular response | 1 | Solved |
3. Unit and sign normalization
- Charge magnitude in microcoulombs is multiplied by 1e-6.
- Speed in km/s is multiplied by 1000 and B in mT by 1e-3.
- Angles are converted to radians only inside the sine function; the table remains labeled in degrees.
4. Current numerical substitution
5. Independent reconciliation
HOW TO USE THIS CALCULATOR
Five steps from measured inputs to a defensible result
- Enter nonnegative charge magnitude, speed, and field for the fixed experimental basis.
- Choose a reference angle whose current force matters to the decision.
- Select an integer angle step that divides 180 so both endpoints are guaranteed.
- Use the normalized column to compare curve shape separately from force scale.
- Export the table and verify the 0/180 endpoints and theta versus 180-theta symmetry before plotting elsewhere.
ELECTROMAGNETIC FOUNDATIONS
Concepts that control this specific model
- The curve is a sine response
- Force is zero for parallel and antiparallel motion and reaches its envelope at 90 degrees.
- Magnitude removes charge sign
- Positive and negative charges share the same magnitude curve but have opposite force directions.
- The envelope is multiplicative
- Changing |q|, v, or B rescales every row by the same factor.
- Angular symmetry is exact
- sin(theta) equals sin(180 degrees - theta), so paired rows must match.
- Sampling resolution is a reporting choice
- A finer angle step adds rows but does not change the underlying equation.
DEEP ANALYSIS 1
Why a table can be better than a decorative graph
Exact current values, units, reference-row labeling, and export fidelity are directly inspectable; external tools can plot the same rows without digitizing pixels.
DEEP ANALYSIS 2
Zero-scale boundaries remain valid
If |q|, v, or B is zero, every force row is zero and the normalized response is defined as zero to avoid a 0/0 display.
DEEP ANALYSIS 3
This sweep cannot recover vector direction
The scalar curve says how large the force is. Determining the Fx, Fy, and Fz signs requires full vectors and the signed charge in the solver page.
RESULT INTERPRETATION
What the current output does and does not decide
Reference force is one row of the response; maximum force is the fixed |q|vB envelope at 90 degrees.
Point count includes the reference angle when it is not already present in the regular step sequence, preventing the headline result from becoming disconnected from the export table.
REAL USE CASES
Two decisions with different boundary conditions
Null-alignment calibration
At 0 and 180 degrees the ideal force is zero. A measured nonzero response there can indicate angular offset, stray transverse field, or a force not included in this model.
EVIDENCE AND DATA QUALITY
What to retain with the exported result
Retain the fixed scale inputs, angle convention, step size, reference-row marker, axis definition used by any downstream plot, and exported endpoint/symmetry check. Record angular calibration uncertainty separately.
LIMITS AND EXCLUSIONS
Where this physical model stops
- Produces a scalar magnitude table, not a force-direction vector.
- Assumes |q|, speed, and uniform B remain constant throughout the angle sweep.
- Excludes electric force, field gradients, relativistic momentum, and particle trajectories.
- Does not interpolate measurements or propagate angle uncertainty.
- The table is graph-ready data; this wave intentionally adds no custom interactive chart runtime.
TERMS USED HERE
Six terms that keep the calculation unambiguous
- Angle sweep
- Ordered evaluation of one equation across a set of angles.
- Force envelope
- Maximum possible magnitude |q|vB for the fixed scale inputs.
- Reference angle
- User-selected angle reported in the headline result and table.
- Normalized force
- Force divided by the maximum envelope.
- Step size
- Angular spacing between regular table rows.
- Symmetry pair
- Angles theta and 180 degrees - theta with equal sine values.
RELIABLE SOURCES
References supporting the equation and units
FREQUENTLY ASKED QUESTIONS
Questions specific to this calculation
Why is the curve zero at 180 degrees?
Velocity is antiparallel to B, so sin(180 degrees) is zero just as it is for parallel motion.
Why is 90 degrees the maximum?
The velocity is entirely transverse to B and sin(90 degrees) equals one.
Why must the step divide 180?
That rule guarantees a regular grid containing both physical endpoints.
What if my reference angle is not on the step grid?
The calculator inserts a dedicated reference row and marks its point type.
Can charge magnitude be zero?
Yes. It is a valid zero-force boundary and all force rows become zero.
Where is the actual graph?
Under the fifth-wave rule this page provides exact responsive table data and one static editorial illustration, not a custom interactive visualization.
IMPORTANT BOUNDARY
Use the result as analysis, not certification
This ideal scalar angle sweep is not a vector trajectory, magnet alignment certification, uncertainty analysis, or substitute for measured field mapping.