An electromagnetic wave traveling in \( x \)-direction is described by magnetic field \( B_{z} = [10^{-7}\sin(\omega t - kx)]\ \mathrm{T} \). The maximum magnetic force experienced by a proton moving with a speed of \( 2\times10^{7}\ \mathrm{m/s} \) along \( y \)-direction in this region of magnetic field is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 3.2\times10^{-19}\ \mathrm{N} \)
The magnetic force on a moving charge is \( F = qvB\sin\theta \). The proton moves along \( y \) and \( \vec{B} \) is along \( z \), so \( \theta = 90^{\circ} \). The force is largest when the field is at its amplitude, \( B_{0} = 10^{-7}\,\mathrm{T} \).
\( F_{\max} = evB_{0}\sin90^{\circ} \)
\( F_{\max} = (1.6\times10^{-19}\,\mathrm{C})(2\times10^{7}\,\mathrm{m\,s^{-1}})(10^{-7}\,\mathrm{T}) \)
\( F_{\max} = 3.2\times10^{-19}\,\mathrm{N} \)