Radius after Electric Acceleration
For a particle starting from rest and accelerated through potential difference V, K = |q|V. Non-relativistically, p = sqrt(2m|q|V), so perpendicular entry gives r = sqrt(2mV/(|q|B^2)).
Why this shows up in the exam
Mass-spectrometer input calculations · Radius-versus-energy graph questions · Finding unknown ion mass or charge
Learn the idea
Acceleration through a voltage sets kinetic energy, which then sets the magnetic orbit radius. A voltage gives the particle energy before the magnetic field bends it. Combining the energy step with the radius step avoids guessing how mass, charge, voltage, and field scale.
🧠 Memory hook: Voltage gives energy first; magnetic field bends second.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- K = |q| V — kinetic energy gained from rest through potential difference magnitude V
- p = sqrt(2 m |q| V) — non-relativistic momentum after acceleration
- r = sqrt(2 m V/(|q| B²)) — orbit radius for perpendicular entry after voltage acceleration
How to approach it
- 1Convert voltage gain to kinetic energy
- 2Find momentum or speed
- 3Insert it into r = p/(|q|B)
Common slip-ups that cost marks
- •Writing r proportional to V instead of sqrt(V)
- •Losing the absolute value of charge in energy
- •Using the formula for a particle that did not start from rest
🌟 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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