A beam of protons moves undeflected along the positive x-axis in a region with crossed uniform electric and magnetic fields. The electric field is directed along the positive z-axis. If the electric field is suddenly switched off, consider the following statements regarding the system: A. The magnetic field is directed along the positive y-axis. B. The magnetic field is directed along the negative y-axis. C. The prot

Step-by-step solution

For the protons to move undeflected, the net force must be zero. The electric force and magnetic force must be equal and opposite. The electric force on a proton (positive charge) is F _E = q E = qE k (along the positive z-axis). Therefore, the magnetic force must be F _B = -qE k (along the negative z-axis). Using the Lorentz force formula F _B = q( v B ) , we have: -qE k = q(v i B ) This implies - k = i B . Since i (- j ) = - k , the magnetic field is directed along the negative y-axis ( - j ). Thus, statement B i