The Memory Trick
Right-Hand Rule — Fingers, Curl, Thumb
The magnetic force on a charge is F = qv × B, with magnitude F = qvB sin θ. For a current-carrying wire it is F = IL × B (magnitude ILB sin θ). The direction comes from your RIGHT hand: point your fingers along v (or the current), curl them toward B, and your thumb points along the force on a POSITIVE charge.
1
Point your fingers along the motion
Aim the fingers of your right hand in the direction the positive charge moves — or the direction of conventional current in a wire.
2
Curl toward the field
Rotate your hand so your fingers can curl from the velocity direction toward the magnetic field direction B through the smaller angle.
3
Your thumb is the force
Your extended thumb now points along the magnetic force on a positive charge. The force is always perpendicular to BOTH v and B.
Check with coordinates: v along +x and B along +y gives F along +z, because x̂ × ŷ = ẑ.
4
Flip for negative charges
For an electron (negative charge), do the same steps and then reverse the direction — or use your LEFT hand.
5
Know the special cases
If v is parallel or antiparallel to B, sin θ = 0 and the force is ZERO. Because the force is always perpendicular to velocity, it does no work: it changes a charge's direction but never its speed, which is why charges in a uniform field move in circles of radius r = mv/(qB).
🏥 Worked Example
A proton moves east at 2.0 × 10⁶ m/s through a uniform 0.50 T magnetic field pointing north. Find the magnitude and direction of the magnetic force. What changes for an electron with the same velocity?
STEP 1
Find the magnitude — the field is perpendicular to the velocity, so sin θ = 1: F = qvB = (1.6 × 10⁻¹⁹ C)(2.0 × 10⁶ m/s)(0.50 T) = 1.6 × 10⁻¹³ N.
STEP 2
Apply the right-hand rule — fingers point east, curl toward north — the thumb points straight UP (east × north = up).
STEP 3
Switch to the electron — same magnitude, 1.6 × 10⁻¹³ N, but the negative charge reverses the direction: the force points DOWN.
CONCLUDE
The proton is pushed upward and the electron downward. Neither particle speeds up or slows down — the force only bends their paths.
📌 Exam Application
Expect direction questions with 'into the page' (⊗) and 'out of the page' (⊙) symbols, wire-in-a-field questions using F = ILB sin θ, and conceptual questions about why magnetic forces do no work. Always check the sign of the charge before giving your final direction.
⚠️ Most Common Magnetic Force Direction Mistakes
The force is never along B — it is perpendicular to it. Students often point the thumb along the field, or forget to reverse the direction for electrons. And a charge moving parallel to the field feels no magnetic force at all.