Question

a 10 eV electron is circulating in a plane at right angles to a uniform field of magnetic induction 10^-4 Tesla (= 1 gauss), the orbital radius of electron is:-
a) 11 cm b) 18 cm
c) 12 cm d) 16 cm

(correct answer is option a......please explain )

Answer 1

When an electron is circulating in uniform magnetic field perpendicular to it then

$F_{mag} = F_{centripetal$

$qvBsin\theta = \frac{mv^2}{R}$

here angle = 90 degree as it is revolving perpendicular to field

$qvB = \frac{mv^2}{R}$

$R = \frac{mv}{qB}$

now we also know that

$mv = \sqrt{2*m*KE}$

given that

$KE = 10eV = 1.6*10^{-18} J$

$m = 9.1* 10^{-31} kg$

$mv = \sqrt{2*9.1*10^{-31}*1.6*10^{-18}}$

$mv = 1.706*10^{-24}$

now radius is given by above formula

$R = \frac{1.706 * 10^{-24}}{1.6*10^{-19}* 10^{-4}}$

R = 10.66 cm which is approximately 11 cm

so radius of orbit will be 11 cm(approx)

Answer 2

Answer: (a) 11cm

Explanation: Refer the image below for the answer