Question

At what angle will the electrons leave the uniform electric field at the end of the parallel plates? Assume the plates are 4.9 cm long, E=5.0\times10^3 and v_0=1.00\times10^7 m/s. Ignore fringing on the field.

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asked 2021-04-03

At what angle will the electrons leave the uniform electric field at the end of the parallel plates? Assume the plates are 4.9 cm long, \(\displaystyle{E}={5.0}\times{10}^{{3}}\) and \(\displaystyle{v}_{{0}}={1.00}\times{10}^{{7}}\) m/s. Ignore fringing on the field.
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Answers (1)

2021-04-05
\(\displaystyle{m}{a}={q}{E}\)
\(\displaystyle{a}={\frac{{{q}{E}}}{{{m}}}}={\frac{{{1.6}\cdot{10}^{{-{19}}}{5}\cdot{10}^{{3}}}}{{{9.1}\cdot{10}^{{-{31}}}}}}\)
\(\displaystyle{a}={\frac{{{q}{E}}}{{{m}}}}={8.79}\cdot{10}^{{{15}}}\frac{{m}}{{s}^{{2}}}\)
We can find the exit velocity:
\(\displaystyle{v}^{{2}}={{v}_{{0}}^{{2}}}+{2}{a}{d}\)
\(\displaystyle{v}^{{2}}={\left({1}\cdot{10}^{{7}}\right)}^{{2}}+{2}\cdot{8.79}\cdot{10}^{{{15}}}\cdot{0.0049}\)
\(\displaystyle{v}={1.364}\cdot{10}^{{7}}\frac{{m}}{{s}}\)
\(\displaystyle\theta={{\tan}^{{-{1}}}{\left({\frac{{{v}}}{{{v}_{{0}}}}}\right)}}\)
\(\displaystyle\theta={{\tan}^{{-{1}}}{\left({\frac{{{1.364}\cdot{10}^{{7}}}}{{{1}\cdot{10}^{{7}}}}}\right)}}\)
\(\displaystyle\theta={53.75}^{\circ}\)
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