A beam of α particles projected along the +x axis in a magnetic field experiences a force along the +y axis. The direction of the magnetic field would be:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Negative z axis
The magnetic force on a moving charge is \( \vec{F} = q(\vec{v}\times\vec{B}) \), so it is perpendicular to both \( \vec{v} \) and \( \vec{B} \). An α particle is positively charged, so \( \vec{F} \) points along \( \vec{v}\times\vec{B} \).
Take \( \vec{v} = v\hat{x} \) and \( \vec{F} \) along \( +\hat{y} \). With \( \hat{x}\times\hat{z} = -\hat{y} \), a field along \( -\hat{z} \) gives:
\( \vec{v}\times\vec{B} = vB\,\hat{x}\times(-\hat{z}) = +vB\,\hat{y} \)
which is the observed direction of the force, so \( \vec{B} \) is along the negative z axis.
Shortcut: The force is perpendicular to both \( \vec{v} \) and \( \vec{B} \). A field along the x axis gives no force (it is parallel to \( \vec{v} \)) and a field along the y axis would give a force along z, so only \( \pm z \) remain; the right-hand rule \( \hat{x}\times\hat{z} = -\hat{y} \) then fixes the sign.