Moving Charges and Magnetism - Result Question 22

22. 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 the electron is

[1996]

(a) $12 cm$

(b) $16 cm$

(c) $11 cm$

(d) $18 cm$

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Answer:

Correct Answer: 22. (c)

Solution:

  1. (c) K.E. of electron $=10 eV$

$\Rightarrow \frac{1}{2} m v^{2}=10 eV$

$\Rightarrow \frac{1}{2}(9.1 \times 10^{-31}) v^{2}=10 \times 1.6 \times 10^{-19}$

$\Rightarrow v^{2}=\frac{2 \times 10 \times 1.6 \times 10^{-19}}{9.1 \times 10^{-31}}$

$\Rightarrow v^{2}=3.52 \times 10^{12} \Rightarrow v=1.88 \times 10^{6} m$

Also, we know that for circular motion

$\frac{m v^{2}}{r}=B e v \Rightarrow r=\frac{m v}{B e}=11 cm$