Revision summary

Name the source field, the selected body and the direction of conventional current or particle velocity. Calculate a force magnitude and a direction, then choose the motion or measurement model.

Uniform electric motion

A positive charge is forced along E and a negative charge against E, including when initially stationary. With perpendicular entry and no other significant force, the field-perpendicular velocity component is constant while the field-parallel component changes. The path is parabolic and total speed can change. Outside the ideal field, continue along the exit tangent.

Field patterns and directions

• Long straight wire: concentric field circles; right thumb follows current and curled fingers give B. Out-of-page current gives anticlockwise field in that view.
• Flat circular coil: central axial field with external return paths. Anticlockwise current seen at a face gives central field towards that observer.
• Long solenoid: approximately uniform interior away from ends, with weaker returning field outside. The grip-rule thumb gives the interior direction and points towards its north end.

Field lines are not particle tracks. A dot means the labelled quantity points out of the page and a cross means into it. Distinguish the views before comparing a face diagram with an axial section.

Conductor force and the current balance

The angle is between conventional current and the external B. Fleming's left-hand rule uses first finger for field, second for conventional current and thumb for conductor force; use the current's perpendicular component for a non-right angle. Parallel or antiparallel current gives zero force. Reversing one of I or B reverses the force; reversing both restores it.

In the shown current balance, an upward wire force produces a downward reaction on the separately weighed magnet. Convert its baseline-subtracted display change from grams to kilograms and use F = gΔm for the stated upward wire-force reference. At fixed perpendicular length, the F-against-I gradient is Bl, so divide by l to obtain B.

Keep supports separate, return wires outside the active field and geometry fixed. Check current-off drift, ranges, resolution, heating, fringing and contact forces. A changed balance display is not a changed physical mass; actual nonzero intercepts and anomalies need investigation.

Magnetic motion and velocity selection

For positive-charge motion, use the conventional-current force direction; reverse it once for a negative charge with the same velocity. A stationary charge or velocity parallel to B gives zero magnetic force. Magnetic force does no work: it changes velocity direction while speed remains constant. It is the inward force, not an extra force in addition to a centripetal force.

For the electron semicircle in x > 0, the exit lies 2r below entry and its velocity is left. Radius and entry-to-exit separation are different. Outside the ideal field, the path is a straight tangent.

This requires the intended incident direction, mutually perpendicular velocity and fields, and nonzero charge. The selected speed is independent of mass and charge magnitude. Off-speed force comparisons give the initial deflection, not automatically a full path or a process that brings every particle to the selected speed.

Quantity and unit reference

The supplied electron constants are e = 1.60 × 10^-19 C and m_e = 9.11 × 10^-31 kg. Convert 1 mT = 10^-3 T, 1 µT = 10^-6 T, 1 µWb = 10^-6 Wb, 1 ns = 10^-9 s and 1 g = 10^-3 kg before using SI equations.

For the supplied uniform perpendicular-area example, Φ = BA: local B and the flux through an area are distinct quantities. The units are 1 T = 1 kg s^-2 A^-1 and 1 Wb = 1 kg m² s^-2 A^-1.