Finite Magnetic Region and Arc Geometry
Within a uniform field region and for perpendicular motion, the trajectory is an arc of radius r = p/(|q|B). Entry tangent, circle center, chord, sagitta, and boundary width determine exit coordinates and deflection.
Why this shows up in the exam
Detector-position problems · Interface motion across two field strengths · Minimum-width magnetic-region design
Learn the idea
A particle inside a bounded magnetic field follows a circular arc whose intersections are fixed by geometry. The field supplies the circle, but the region boundaries decide where the particle exits or re-enters. A clean circle sketch often matters more than extra algebra.
🧠 Memory hook: Find the circle first; let the boundary cut the arc.
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) — arc radius inside the field
- chord = 2 r sin(phi/2) — straight separation of two points subtending central angle phi
- sagitta = r[1 - cos(phi/2)] — arc height for a symmetric chord geometry
How to approach it
- 1Find radius and bending side
- 2Locate the center perpendicular to entry velocity
- 3Use circle-boundary geometry for the requested distance
Common slip-ups that cost marks
- •Assuming every path is a semicircle
- •Placing the circle center on the wrong side of the entry tangent
- •Using full-circle displacement instead of boundary-to-boundary displacement
🌟 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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