- #1

fluidistic

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## Homework Statement

There's a uniform EM field given by ##\vec E=E\hat y##, ##\vec B=B\hat z##

with respect to an inertial reference frame K.

A charged particle with rest mass m and charge q>0 moves in the field with an initial velocity orthogonal to ##\vec B##.

1)Write down the equation of motion of the particle.

2)Show that if ##E<cB## then there exist an inertial frame of reference K' that moves with constant velocity with respect to K such that the electric field vanishes.

3)Solve the equation of motion in K' and show that the trajectory is circular in a plane orthogonal to ##\vec B##, with a constant frequency of oscillation.

## Homework Equations

Lorentz force.

## The Attempt at a Solution

1)##\frac{d\vec p}{dt}=q(E\hat y + \vec v \times B \hat k)##. I can choose ##\vec v(t=0)## to be worth ##v_0 \hat x## if I have to solve that equation of motion. I am not sure whether my answer is ok or if they want it more simplified.

2)Not sure how to tackle this one. Should I solve the equation in 1) (which I'm not even sure how to do due to the term involving the velocity) and realize that if I move with constant velocity with respect to K then ##\vec E## vanishes? Or should I start with E<cB and simplify some things out?

Thank you.

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