Novel Solutions
Charged particle in combined E and B fields
The Spiral That Never Happens
Crossed electric and magnetic fields sit right at the JEE Advanced ceiling — the same E×B drift trick underlies mass spectrometers and magnetrons.
A charged particle of mass m and charge q is released from rest at the origin, in a region with a uniform electric field E (along y) and a uniform magnetic field B (along z, perpendicular to E). Describe its subsequent motion.
The intuitive guess
"B always acts perpendicular to velocity and does no work, while E keeps doing work as the particle drifts along y — so the particle should accelerate steadily, curving into an ever-tightening spiral that grows without bound." In fact the particle’s speed never exceeds 2E/B, and it periodically returns all the way to rest.