A proton traveling to the right along the x-axis enters a region where there is a magnetic field directed upward along the y-axis. What is the direction of the force on the proton and draw a diagram of it. If the direction changes to proton moving straight upward ( away from ground) into a magnetic field that points from east to west, what direction and diagram of the force? I am not sure how to show some directions and getting confused.
The proton is subjected to the magnetic force F = qv × B, called the Lorentz force. The direction of this force is obtained from the cross product of v and B resulting in a vector perpendicular to the plane formed by these vectors. In practice, to determine the direction, we apply the rule of the right hand: We rotate with the four fingers, the vector v on the vector B at the lower angle, then the thumb indicates the direction and sense of F.
In the first case, the force is directed in the positive direction of z axis, as shown in the attached, Fig 1
In the second case, the force is directed towards the south as shown in the attached, Fig 2
A moving charge entering a region where there is a magnetic field will experience a force called Lorenz's force. It is perpendicular to both the velocity of a charge to the direction of the field, which means it is perpendicular to the plane containing both vectors (velocity and field.)
If the charge is positive (which it is in the case of a proton), the direction of the force can be determined by the right-hand rule.
The picture in the document LorenzForce_1 illustrates a case where the velocity of the proton is along x-axis and the field is along y-axis. Then, the force on the proton will be perpendicular to the coordinate plane xy and it will point out of the screen (or page) and at the viewer.
The picture in the document LorenzForce_2 illustrates a case where the velocity of the proton is upward and the magnetic field is directed from East to West. Then, the magnetic force on the proton will be pointing South.
Please see the reference website for a detailed explanation of how to use a right-hand rule.