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.

Other

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.

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:
$$\displaystyle{v}^{{2}}={{v}_{{0}}^{{2}}}+{2}{a}{d}$$
$$\displaystyle{v}^{{2}}={\left({1}\cdot{10}^{{7}}\right)}^{{2}}+{2}\cdot{8.79}\cdot{10}^{{{15}}}\cdot{0.0049}$$
$$\displaystyle{v}={1.364}\cdot{10}^{{7}}\frac{{m}}{{s}}$$
$$\displaystyle\theta={{\tan}^{{-{1}}}{\left({\frac{{{v}}}{{{v}_{{0}}}}}\right)}}$$
$$\displaystyle\theta={{\tan}^{{-{1}}}{\left({\frac{{{1.364}\cdot{10}^{{7}}}}{{{1}\cdot{10}^{{7}}}}}\right)}}$$
$$\displaystyle\theta={53.75}^{\circ}$$