Question 652: Electrostatics & Capacitance

Question

A uniform electric field of 10 N/C is created between two parallel charged plates (as shown in figure). An electron enters the field symmetrically between the plates with a kinetic energy 0.5 eV. The length of each plate is 10 cm. The angle ($$	heta$$) of deviation of the path of electron as it comes out of the field is ___________ (in degree).

Accepted Answer

$$
\begin{aligned}
& 0.5 \mathrm{e}=\frac{1}{2} \mathrm{mv}_{\mathrm{x}}^2 \Rightarrow \mathrm{v}_{\mathrm{x}}=\sqrt{\frac{\mathrm{e}}{\mathrm{m}}} \\
& 	ext { Along } \mathrm{x} \mathrm{L}=\mathrm{v}_{\mathrm{x}} \mathrm{t}=\sqrt{\frac{\mathrm{e}}{\mathrm{m}}} \mathrm{t} \\
& 	ext { Along y } \mathrm{v}_{\mathrm{y}}=\frac{\mathrm{eE}}{\mathrm{m}} \mathrm{t} \\
& \operatorname{dividing} \frac{\mathrm{v}_{\mathrm{y}}}{\mathrm{L}}=\mathrm{E} \sqrt{\frac{\mathrm{e}}{\mathrm{m}}}=\mathrm{E} v_{\mathrm{x}} \\
& \Rightarrow \operatorname{tan} 	heta=\frac{\mathrm{v}_{\mathrm{y}}}{\mathrm{v}_{\mathrm{x}}}=\mathrm{E} 	imes \mathrm{L}=10 	imes 0.1=1 \\
& 	heta=45^{\circ}
\end{aligned}
$$

Electrostatics & Capacitance

Integer / Numeric Answer Type