# Trajectory of charged particles in a magnetic field?

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?

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.

Nugatory said:
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.

PeroK

## 1. What is the trajectory of a charged particle in a magnetic field?

The trajectory of a charged particle in a magnetic field is a curved path, known as a helix, due to the interaction between the magnetic field and the particle's electric charge.

## 2. How does the strength of the magnetic field affect the trajectory of a charged particle?

The strength of the magnetic field affects the radius of the helix, with a stronger magnetic field resulting in a smaller radius and a weaker magnetic field resulting in a larger radius.

## 3. What is the role of the particle's velocity in its trajectory in a magnetic field?

The particle's velocity determines the pitch (spacing) of the helix, with a higher velocity resulting in a smaller pitch and a lower velocity resulting in a larger pitch.

## 4. How does the charge of the particle affect its trajectory in a magnetic field?

The charge of the particle determines the direction of the helix, with a positively charged particle following a helix in one direction and a negatively charged particle following a helix in the opposite direction.

## 5. What is the equation for calculating the trajectory of a charged particle in a magnetic field?

The equation for calculating the trajectory of a charged particle in a magnetic field is given by: r = (mv sinθ) / (qB), where r is the radius of the helix, m is the mass of the particle, v is its velocity, θ is the angle between the velocity and the magnetic field, q is the charge of the particle, and B is the strength of the magnetic field.