A very long straight wire carries a current (I) directed along positive Y-axis. A point charge +Q moves with velocity (v) along X-axis. The direction of force on the charge at point (5, 0, 0) m is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → along positive y-axis
First find the direction of the magnetic field of the wire at the charge, then use the Lorentz force \( \vec{F} = Q\,\vec{v}\times\vec{B} \).
The field of a straight current is along \( \hat{I}\times\hat{r} \), where \( \hat{r} \) points from the wire to the point. Here the current is along \( \hat{\jmath} \) and the point (5, 0, 0) lies along \( \hat{\imath} \) from the wire.
\( \displaystyle \hat{B} = \hat{\jmath}\times\hat{\imath} = -\hat{k} \)
The charge moves along the x-axis, taken as the positive x-direction, so \( \vec{v} = v\,\hat{\imath} \).
\( \displaystyle \vec{F} = Q\,(v\,\hat{\imath})\times(-B\,\hat{k}) = -QvB\,(\hat{\imath}\times\hat{k}) = -QvB\,(-\hat{\jmath}) = QvB\,\hat{\jmath} \)
The force is along the positive y-axis, that is, parallel to the current in the wire.