6.3FieldsStretch

Force on a Moving Charge

A lone moving charge, not confined to any wire, still feels a force in a magnetic field. Because that force is always perpendicular to velocity, it never speeds a charge up or slows it down — it only steers it, bending its path into a perfect circle.

40 min Video by Science Ready Module 6.3 Magnetic fields

Charges in Magnetic Fields: Forces & Uniform Circular MotionWatch the full walkthrough before the notes below.

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What you'll be able to do

Use $F = B Q v sin θ$
Explain why the magnetic force on a moving charge does no work
Explain why a charge moving perpendicular to a field follows a circular path
Use $r = \frac{m v}{B Q}$

Force on a moving charge

A charge moving through a magnetic field experiences a force that is greatest when velocity is perpendicular to the field.

F = B Q v sin θ

Force on a moving charge.

1Use

F = B Q v

(θ=90°).

F = 0.30 \times 1.60 \times 1 0^{- 19} \times 2.5 \times 1 0^{6}

Answer

F = 1.2 \times 1 0^{- 13}

Circular motion in a magnetic field

Because the magnetic force is always perpendicular to velocity, it does no work and only changes direction, not speed — exactly the condition for circular motion, with the magnetic force providing the centripetal force.

r = \frac{m v}{B Q}

Radius of circular path (v ⊥ B).

1Use

r = \frac{m v}{B Q}

r = \frac{1.67 \times 1 0 ^{- 27} \times 4.0 \times 1 0 ^{6}}{0.50 \times 1.60 \times 1 0 ^{- 19}}

Answer

r \approx 0.0835

Tip — A heavier (or faster) particle curves in a LARGER circle for the same field and charge — r=mv/(BQ) increases with mass and speed.

Equation recap

F = B Q v sin θ

Force on a moving charge.

r = \frac{m v}{B Q}

Radius of circular path.

Common mistakes to avoid

Thinking the magnetic force changes a charged particle’s speed.

The force is always perpendicular to velocity, so it does no work and never changes speed.

Assuming a heavier particle curves in a smaller circle.

r=mv/(BQ) increases with mass — heavier particles curve in LARGER circles.

Key takeaways

F = BQvsinθ; maximum when v is perpendicular to B.
The magnetic force does no work — it changes direction, not speed.
A charge moving perpendicular to a uniform field follows a circular path, r = mv/(BQ).

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Force on a Moving Charge

40 min Video by Science Ready Module 6.3 Magnetic fields