Physics - Magnetism Question with Solution | TestHub

The initial magnetic force is ${\vec{F}}_M=q(\vec{v}\times \vec{B})=q(v_0\hat{k}\times B_0\hat{j})=q{v}_0{B}_0(\hat{k}\times \hat{j})=-q{v}_0{B}_0\hat{i}$. So A is correct. The electric force ${\vec{F}}_E=q\vec{E}=q{E}_0\hat{i}$ acts along the x-axis. As the particle moves, its velocity will acquire an x-component, and the electric force will do work, thereby changing the particle's kinetic energy and thus its speed. So B is correct. The condition $E_0=v_0{B}_0$ means the initial electric force and magnetic force in the x-direction cancel out. However, the particle's velocity is perpendicular to the magnetic field, and the electric field is also perpendicular to the magnetic field. This setup leads to a complex trajectory, not a simple helix, as a helix requires a velocity component parallel to the magnetic field. So C is incorrect. By the definition of the cross product, the magnetic force ${\vec{F}}_M=q(\vec{v}\times \vec{B})$ is always perpendicular to both $\vec{v}$ and $\vec{B}$. So D is correct.