An alpha particle is moving in a magnetic field, \( (3\hat{\imath} + 2\hat{\jmath})\,\mathrm{T} \) with the velocity \( (7\times10^{5}\,\hat{\imath})\,\mathrm{m/s} \). The magnetic force acting on the particle is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 4.48\times10^{-13}\,\hat{k}\,\mathrm{N} \)
The magnetic force on a moving charge is \( \vec{F} = q\,(\vec{v}\times\vec{B}) \). An alpha particle is a helium nucleus with charge \( q = 2e = 3.2\times10^{-19}\,\mathrm{C} \).
\( \displaystyle \vec{v}\times\vec{B} = 7\times10^{5}\,\hat{\imath}\times(3\hat{\imath} + 2\hat{\jmath}) = 14\times10^{5}\,(\hat{\imath}\times\hat{\jmath}) = 1.4\times10^{6}\,\hat{k} \)
Here \( \hat{\imath}\times\hat{\imath} = 0 \) and \( \hat{\imath}\times\hat{\jmath} = \hat{k} \).
\( \displaystyle \vec{F} = 3.2\times10^{-19} \times 1.4\times10^{6}\,\hat{k} = 4.48\times10^{-13}\,\hat{k}\,\mathrm{N} \)