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4.Moving Charges and Magnetism
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In an experiment, electrons are accelerated, from rest, by applying, a voltage of $500 \,V.$ Calculate the radius of the path if a magnetic field $100\,mT$ is then applied. [Charge of the electron $= 1.6 \times 10^{-19}\,C$ Mass of the electron $= 9.1 \times 10^{-31}\,kg$ ]
A
$7.5\times 10^{-3}\,m$
B
$7.5\times 10^{-2}\,m$
C
$7.5\,m$
D
$7.5\times 10^{-4}\,m$
(JEE MAIN-2019)
Solution
${{\text{k}}_{\text{e}}} = \frac{{{{\text{p}}^2}}}{{2{{\text{M}}_{\text{e}}}}} = 500\,{\text{e}} \ldots ({\text{i}})$
$\ \,{\text{R}} = \frac{{\text{p}}}{{{\text{eB}}}} = \frac{{1000{{\text{m}}_{\text{e}}}{\text{e}}}}{{{\text{eB}}}}$
$ = \frac{{1010 \times 9.1 \times {{10}^{ – 31}}}}{{1.6 \times {{10}^{ – 19}}}}$
$ = 100 \times 7.541 \times {10^{ – 6}}$
Standard 12
Physics
