What is the radius of the path of an electron (mass $9 \times 10^{-31}\;kg$ and charge $1.6 \times 10^{-19} \;C )$ moving at a speed of $3 \times 10^{7} \;m / s$ in a magnetic field of $6 \times 10^{-4}\;T$ perpendicular to it? What is its frequency? Calculate its energy in $keV$. ( $\left.1 eV =1.6 \times 10^{-19} \;J \right)$
What is the radius of the path of an electron (mass $9 \times 10^{-31}\;kg$ and charge $1.6 \times 10^{-19} \;C )$ moving at a speed of $3 \times 10^{7} \;m / s$ in a magnetic field of $6 \times 10^{-4}\;T$ perpendicular to it? What is its frequency? Calculate its energy in $keV$. ( $\left.1 eV =1.6 \times 10^{-19} \;J \right)$
$r=m v /(q B)$$=9 \times 10^{-31} kg \times 3 \times 10^{7} m s ^{-1} /\left(1.6 \times 10^{-19} C \times 6 \times 10^{-4} T \right)$
$=26 \times 10^{-2}\, m =26 \,cm$
$v=v /(2 \pi r)=2 \times 10^{6}\, s ^{-1}$$=2 \times 10^{6} Hz =2 \,MHz$
$E=(1 / 2) m v^{2}=(1 / 2) 9 \times 10^{-31} \,kg \times 9 \times 10^{14} \,m ^{2} / s ^{2}$$=40.5 \times 10^{-17}\, J$
$\approx 4 \times 10^{-16} \,J =2.5 \,keV$
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