General Motion in Combined Electric and Magnetic Fields
The total Lorentz force is q(E + v cross B). The electric term can do work at rate qE dot v; the magnetic term has zero power. Special geometries should be solved from this vector equation rather than from a memorized path name.
Why this shows up in the exam
Predicting straight, helical, cycloidal, or drift motion · Handling parallel E and B · Checking force directions for positive and negative ions
Learn the idea
In combined fields, electric force can change energy while magnetic force mainly redirects motion. Treat the two field effects separately before combining them. Parallel electric acceleration, crossed-field drift, and curved motion arise from the relative directions of E, B, and the initial velocity.
🧠 Memory hook: Electric field can change speed; magnetic field turns the velocity.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- F = q(E + v cross B) — total electromagnetic force on a point charge
- P = q E dot v — only the electric part changes kinetic energy
- a_parallel = q E_parallel/m — parallel electric acceleration in the non-relativistic regime
How to approach it
- 1Write the full Lorentz force
- 2Resolve along and across B
- 3Identify which component changes energy and then infer the path
Common slip-ups that cost marks
- •Naming the path before resolving field directions
- •Assuming E and B forces always cancel
- •Forgetting that a released particle initially has no magnetic force
🌟 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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