Question #199251

An electron moves in uniform magnetic field with a speed of 5ยท106 m/s along the x axis. The magnetic field strength is 0.050 T, directed at an angle of 45ยฐ to the x axis and lying in the xy plane. Calculate the magnetic force ๐น on and acceleration ๐‘Ž of the electron.


1
Expert's answer
2021-05-27T08:29:40-0400

(a) We can find the magnetic force on the electron as follows:


F=qvBsinฮธ,F=qvBsin\theta,F=1.6โ‹…10โˆ’19 Cโ‹…5โ‹…106 msโ‹…0.05 Tโ‹…sin45โˆ˜=2.83โ‹…10โˆ’14 N.F=1.6\cdot10^{-19}\ C\cdot5\cdot10^6\ \dfrac{m}{s}\cdot0.05\ T\cdot sin45^{\circ}=2.83\cdot10^{-14}\ N.

(b) We can find the acceleration of the electron from Newton's Second Law of Motion:


F=ma,F=ma,a=Fm=2.83โ‹…10โˆ’14 N9.11โ‹…10โˆ’31 kg=3.1โ‹…1016 ms2.a=\dfrac{F}{m}=\dfrac{2.83\cdot10^{-14}\ N}{9.11\cdot10^{-31}\ kg}=3.1\cdot10^{16}\ \dfrac{m}{s^2}.

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