Q 12-04-236JEE MainJEE Main 2017 (9 Apr)Medium
A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is:
Answer: (B) Towards the wire
Let the current be along $+\hat z$. Its field at the charge is azimuthal, $\vec B = B\hat\phi$. For a charge moving radially with velocity $\vec v = \pm v\hat r$,
$$\vec F = q\vec v\times\vec B = \pm qvB(\hat r\times\hat\phi) = \pm qvB\,\hat z$$
For a negative $q$ the force is along $+\hat z$ (the current direction) when $\vec v = -v\hat r$, i.e. when the charge moves **towards** the wire. (Motion parallel to the wire would give a radial force.)
Solution by Sreeraj P, M.Sc Physics