91Ó°ÊÓ

Given information:

Electric field strength is $50,000\mathrm{N}/\mathrm{C}$.

Spacing is $2.0\mathrm{mm}$.

Find:

The objective is to find proton's speed reaches the negative plate.

The particle travels along the field, more toward the capacitor's deleterious anode, in a static electric field. At the expenditure of electrostatic field, it gains angular momentum.

The variation in electromotive force can be computed using equation $(28.10)$:

$$\begin{gathered} \mathrm{Δ}{U}_{\mathrm{e}}=U_{\mathrm{e},\mathrm{f}}−U_{\mathrm{e},\mathrm{i}} \\ =\left(U_0+qEâ‹\dots 0\right)+\left(U_0+qEd\right) \end{gathered}$$

$=−qEd$

We can compute the proton's mobility when it approaches the negatively pole by transforming the difference in electromotive force energy into kinetic energy.

From energy conversation

$(\mathrm{Δ}K+\mathrm{Δ}U=0)$

$\mathrm{Δ}K=−\mathrm{Δ}{U}_{\mathrm{e}}$

$\frac{1}{2}{m}_{\mathrm{p}}{v}_{\mathrm{f}}^2=qEd$

$v_f=\sqrt{\frac{2qEd}{m_p}}$

$=\sqrt{\frac{2×1.602×{10}^{−19}\mathrm{C}×50000\frac{\mathrm{N}}{\mathrm{C}}×2×{10}^{−3}\mathrm{m}}{1.673×{10}^{−27}\mathrm{kg}}}$

localid="1649456505449" $v_{\mathrm{f}}≈1.38×{10}^5\frac{\mathrm{m}}{\mathrm{s}}$