4. In the figure below a high speed positive charge mass \( m \) enters a magnetic field \( \overrightarrow { \mathrm { B} } \) perpendicular to the direction of its velocity. The magnetic field is pointing into the paper. (a) Sketch the trajectory of the particle after entering the magnetic field.  

When a high-speed positive charge enters a magnetic field perpendicular to its velocity, it undergoes circular motion. The magnetic force acts as a centripetal force, directing the charge towards the center of its circular path. As the particle enters the field, sketch the trajectory as a circle with the particle moving in a counter-clockwise direction (assuming the positive charge goes into the field from the left). The radius of this circular path depends on the particle's velocity, charge, and the strength of the magnetic field. The right-hand rule can help you determine the direction of the magnetic force. Point your fingers in the direction of the velocity (to the right if entering from the left), curl them in the direction of the magnetic field (into the paper), and your thumb will point in the direction of the magnetic force acting on the positive charge, which will direct it upwards, creating a circular path.