Charged-Particle Motion by Energy Conservation
If only electrostatic forces do work, K+qV is conserved between points; additional forces or radiation invalidate the simple relation.
Why this shows up in the exam
speed near charged rings or spheres · released-particle turning points · energy in prescribed potential functions
Learn the idea
Electric potential energy can convert to kinetic energy without solving the trajectory. Like a bead sliding down a hill, a charged particle trades qV for kinetic energy. The charge sign decides which direction is downhill in energy.
🧠 Memory hook: Conserve K plus qV; let q carry the sign.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- K_i + qV_i = K_f + qV_f — only conservative electrostatic work
- v_f² = v_i² + (2q/m)(V_i-V_f) — nonrelativistic particle
How to approach it
- 1Write total energy at both endpoints
- 2Insert signed q and potential
- 3Check K_f is nonnegative
Common slip-ups that cost marks
- •Assuming positive charge behavior for an electron
- •Using energy conservation when nonconservative forces matter
- •Taking a square root before checking accessibility
🌟 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.
Two point charges 1 microC and 2 microC are 1 m apart in vacuum. Take k = 9 x 10^9 SI. Find the force magnitude.
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