A constant uniform magnetic field $\mathbf B=\hat{\mathbf z}B$ exists in vacuum. A particle of mass m and small charge q enters with $\mathbf v=\hat{\mathbf x}v_x+\hat{\mathbf z}v_z$. All of B,m,q,$v_x,v_z$ are nonzero. Its eventual trajectory is
Correct answer: (A) helical motion in the z direction
Explanation
The magnetic force $q\mathbf v\times\mathbf B$ is perpendicular to velocity and has no z component. Therefore $v_z$ stays constant.
The transverse component rotates in the xy plane under the magnetic force, forming circular motion of radius $m|v_x|/(|q|B)$. Combining that rotation with uniform z motion produces a helix about the z axis. Hence **A**.
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