Trajectory of charged particles in a magnetic field?

[Adeonaja]

A charge is entering magnetic field perpendicularly! Griffiths says it motion will be circular! But it is accelerated so it must radiate energy and it's motion should be spiral inward?

 

[Nugatory]

Google for "synchrotron radiation"; it does indeed lose energy. Without an exact citation we can't be sure, but chances are that Griffith is considering a situation in which the energy loss to radiation and deviation from the zero-energy-loss trajectory are small enough to ignore.

 

[jtbell]

Google for "synchrotron radiation"

Or look in Griffiths's chapter on radiation near the end of the book.

In my copy of the 3rd edition, he considers synchrotron radiation in Problem 11.16 on page 465, which asks the student to derive the power loss when $\vec v$ and $\vec a$ are perpendicular.