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