The Right-Hand Rules, Sorted Out

You’ll be able to

Apply the right-hand rule for the force on a moving positive charge
Apply the right-hand rule for the field around a current-carrying wire
Handle negative charges and reverse the result correctly

There are two different rules and they answer different questions

Students merge these and then get half the questions wrong. Rule 1 — force on a moving charge: point the fingers along v, curl them toward B, and the thumb gives F for a positive charge. Rule 2 — field around a wire: point the thumb along the current, and the fingers curl in the direction of B looping around the wire. The first produces a single vector perpendicular to two others; the second produces circular loops. Deciding which question you are answering is the first step.

The two magnetic forces

on a charge: F = qvB sin θ · on a current-carrying wire: F = BIL sin θ

θ is the angle between v (or the current) and B. Both forces are ZERO when the motion is parallel to the field, which is a favorite exam case.

Negative charges: solve then flip

The right-hand rule is defined for positive charges. For an electron or any negative charge, apply the rule as normal and then reverse the answer. Do not attempt to use your left hand — mixing conventions mid-problem is how sign errors get in. Solve for a positive charge, state the direction, then flip it, and write down that you have flipped it so a grader can follow.

Why magnetic force does no work

The magnetic force is always perpendicular to the velocity. A force perpendicular to motion does no work, so it cannot change the particle's speed or kinetic energy — only its direction. That is why a charge in a uniform magnetic field moves in a circle at constant speed, and why magnetic forces never appear in energy conservation equations. It is also the sharpest contrast with the electric force, which is along the field and does change speed.

Circular motion in a magnetic field

qvB = mv²/r → r = mv/(qB)

Faster or heavier particles curve less; stronger fields or larger charges curve them more. This single relation drives the mass spectrometer.

Worked example

A proton moves east at 2.0 × 10⁵ m/s through a magnetic field of 0.40 T directed north. Find the magnitude and direction of the force, and the radius of its path. (m = 1.67 × 10⁻²⁷ kg)

1.v is east, B is north, and they are perpendicular, so sin θ = 1.
2.F = qvB = (1.60 × 10⁻¹⁹)(2.0 × 10⁵)(0.40) = 1.28 × 10⁻¹⁴ N.
3.Right-hand rule: fingers east, curl north, thumb points UP. The charge is positive, so no flip.
4.Radius: r = mv/(qB) = (1.67 × 10⁻²⁷)(2.0 × 10⁵) / [(1.60 × 10⁻¹⁹)(0.40)].
5.r = (3.34 × 10⁻²²)/(6.40 × 10⁻²⁰) = 5.2 × 10⁻³ m.

Answer: F = 1.28 × 10⁻¹⁴ N directed upward, and the proton follows a circle of radius about 5.2 mm. An electron in the same situation would feel the same magnitude force directed downward.

Watch out

A charge moving parallel to a magnetic field feels no force at all, since sin 0° = 0. Questions describing motion along the field lines are testing whether you check the angle before reaching for the rule.

Checkpoint

An electron moves north through a magnetic field directed vertically upward. The force on it is:

Checkpoint

A magnetic force cannot change a charged particle's speed because it is always:

Checkpoint

A current flows northward in a long straight wire. Directly above the wire, the magnetic field points:

On the exam

Say out loud which rule you are using and, for a negative charge, write "reversed for negative charge" in your working. Graders follow stated reasoning, and it also stops you from forgetting the flip.

Answer the 3 checkpoints as you read.