Question

A $10eV$ 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 $\left(\frac{1}{2}\times m{v}^2\right)=10eV$
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 $=\frac{m{v}^2}{r}=Bev$.
Therefore $r=\frac{mv}{Be}=\frac{\left(9.1\times 10^{-31}\right)\times \left(1.876\times 10^6\right)}{10^{-4}\times \left(1.6\times 10^{-19}\right)}$
$=11\times 10^{-2}m=11cm$.