Circular Radius from Momentum
For v perpendicular to uniform B, magnetic force supplies centripetal force, giving r = p/(|q|B) = mv/(|q|B) in the non-relativistic limit.
Why this shows up in the exam
Comparing ion-track curvature · Finding momentum from a measured track · Analyzing circular arcs in magnetic regions
Learn the idea
Perpendicular motion in a uniform magnetic field is circular with radius proportional to momentum per unit charge. A faster or heavier particle resists bending, while a larger charge or stronger field bends it more sharply. The sign chooses the turning direction but not the radius magnitude.
🧠 Memory hook: More momentum means a wider circle; more qB means a tighter one.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- r = p/(|q| B) — general momentum-radius relation for perpendicular entry
- r = m v/(|q| B) — non-relativistic form when p = mv
- |q|vB = mv²/r — force balance used to derive the radius
How to approach it
- 1Identify p perpendicular to B
- 2Use magnitude |q| for radius
- 3Handle charge sign separately for the bending direction
Common slip-ups that cost marks
- •Using signed q in a radius magnitude
- •Comparing curvature and radius as if they increase together
- •Forgetting to use only the perpendicular momentum
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A charge of 2 microC moves perpendicular to a 3 T magnetic field at 4 x 10^5 m/s. Find the magnetic force.
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