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Q)

An electron of energy $2000\;eV$ describes a path in magnetic field of flux density $0.2\;T$ What is the radius of this path ?

$\begin{array}{1 1} 7.5 \times 10^4 \;m \\ 7.5 \times 10^{-4}\;m \\ 7.5 \times 10^{5}\;m \\ 7.5 \times 10^{-5}\;m \end{array} $

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A)
Solution :
Given $E'= 2000\;ev$
$\qquad= 2000 \times 1.6 \times 10^{-19}$
$\qquad= 3.2 \times 10^{-16}$
$B= 0.2 \;T$
$E'= \large\frac{1}{2}$$mv^2$
$V= \sqrt{\large\frac{2Ei}{m}}$
$Bev= \large\frac{mv^2}{r}$
$r= \large\frac{mv}{Be}$
$\qquad= \large\frac{m}{Be}\sqrt{ \large\frac{2E^1}{m}}$
$\qquad= \large\frac{\sqrt{2E'm}}{Be}$
$\qquad= \large\frac{\sqrt{2 \times 3.2 \times 10^{-16} \times 9 \times 10^{-31}}}{0.2 \times 1.6 \times 10^{-19}}$
$\qquad= 7.5 \times 10^{-4}$
Answer : $ 7.5 \times 10^{-4}\;m $
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