An electron moves through a uniform electric field E = (2.00î + 5.40ĵ) V/m and a uniform magnetic field B = 0.400k T. Determine the acceleration of the electron when it has a velocity v = 8.0î m/s. (Give each component in m/s2.)
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Question:
An electron moves through a uniform electric field E = (2.00î + 5.40ĵ) V/m and a uniform magnetic field B = 0.400k T. Determine the acceleration of the electron when it has a velocity v = 8.0î m/s. (Give each component in m/s2.)
Answers
Answer:[tex]a=1.75\times 10^{21}\left ( 2\hat{i}5.08\hat{j}\right )[/tex]Explanation:GivenElectric Field [tex]\vec{E}=2\hat{i}+5.4\hat{j}[/tex][tex]\vec{B}=0.4\hat{k}\ T[/tex]velocity [tex]\vec{v}=8\hat{i} m/s[/tex]mass of electron [tex]m=9.1\times 10^{-31} kg[/tex]Force on a charge Particle moving in Magnetic Field[tex]F=e\left [ \vec{E}+\left ( \vec{v}\times \vec{B}\right )\right ][/tex] [tex]a=\frac{e\left [ \vec{E}+\left ( \vec{v}\times \vec{B}\right )\right ]}{m}[/tex][tex]a=\frac{1.6\times 10^{-19}\left [ 2\hat{i}+5.4\hat{j}+\left ( 8\hat{i}\times 0.4\hat{k}\right )\right ]}{9.1\times 10^{-31}}[/tex] [tex]a=1.75\times 10^{21}\left ( 2\hat{i}+5.08\hat{j}\right )\ m/s^2[/tex]
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