An electric field E and a magnetic field B applied on a Proton which m...
Proton Deflection in Electric and Magnetic Fields
E perpendicular to B
If the electric field E is perpendicular to the magnetic field B, the proton will go undeflected through the region. This is because the Lorentz force experienced by the proton is given by F = q(E + V × B), where q is the charge of the proton. Since E and V × B are perpendicular to each other, the Lorentz force is zero.
E parallel to V and perpendicular to B
If the electric field E is parallel to the velocity V of the proton and perpendicular to the magnetic field B, the proton will also go undeflected through the region. This is because the Lorentz force is now given by F = q(E + V × B), but since E is parallel to V, the cross product V × B is zero, and the Lorentz force is again zero.
E, B, and V all perpendicular to each other and V = E/B
If E, B, and V are all mutually perpendicular and V = E/B, the proton will go undeflected through the region. This is because in this case, the Lorentz force simplifies to F = qV × B. Since V and B are perpendicular to each other, the cross product is zero, and the Lorentz force is zero.
E and B both parallel but perpendicular to V
If E and B are both parallel but perpendicular to the velocity V of the proton, the proton will be deflected in a circular path. This is because the Lorentz force is now given by F = qV × B, and since V and B are perpendicular to each other, the force is perpendicular to the velocity of the proton, causing it to move in a circular path.
Overall, the behavior of the proton in electric and magnetic fields depends on the relative orientations of E, B, and V, as well as the direction of the Lorentz force experienced by the proton.