Exercise

Introduction Mutually perpendicular electric and magnetic field is generally referred to as Cross field. In this document we work out the trajectory of a charged particle in a cross field. The charged particle is stationary in the beginning. Problem Let a charged particle with charge $q$ be located at the origin with the magnetic field $\vec{B} = B\vec{k}$ and electric field $\vec{E} = E\vec{j}$. We are interested in working out the trajectory of the charged particle. ...

Introduction In most simplified scenarios we ignore the role of air drag on the body under the influence of gravitataion. A good approximation for the air drag force is that it is proportional to the speed of the body. Calculations Lets suppose a body of mass $m$ is thrown upward with initial speed $v_0$ .The drag force from the air is $\vec{F}=-\alpha m \vec{v}$. Choosing coordinate axis to be such that the upward direction is positive $Z$ axis. ...