Question

A $10\, eV$ electron is circulating in a plane at right angles to a uniform field at magnetic induction $10^{-4} \,Wb / m ^{2}$ (= $1.0$ gauss), the orbital radius of electron is

• A. 11 cm
• B. 18 cm
• C. 12 cm
• D. 16 cm

Answer 1

Answer: (A)

Kinetic energy of electron $\left(\frac{1}{2} \times m v^{2}\right)=10\, eV$
and magnetic induction $( B )=10^{-4}\, Wb / m ^{2}$
Therefore $\frac{1}{2}\left(9.1 \times 10^{-31}\right) v^{2}=10 \times\left(1.6 \times 10^{-19}\right)$
or, $v^{2}=\frac{2 \times 10 \times\left(1.6 \times 10^{-19}\right)}{9.1 \times 10^{-31}}=3.52 \times 10^{12}$
or, $v=1.876 \times 10^{6} m$.
Centripetal force $=\frac{m v^{2}}{r}=B \,e v$.
Therefore $r=\frac{m v}{B e}=\frac{\left(9.1 \times 10^{-31}\right) \times\left(1.876 \times 10^{6}\right)}{10^{-4} \times\left(1.6 \times 10^{-19}\right)}$
$=11 \times 10^{-2} m =11\, cm$.