Question 738: Electrostats & Capacitance

Question

A stream of a positively charged particles having $${q \over m} = 2 	imes {10^{11}}{C \over {kg}}$$ and velocity $${\overrightarrow v _0} = 3 	imes {10^7}\widehat i\,m/s$$ is deflected by an electric field $$1.8\widehat j$$ kV/m. The electric field exists in a region of 10 cm along $$x$$ direction. Due to the electric field, the deflection of the charge particles in the $$y$$ direction is _________ mm.

Accepted Answer

$$
\begin{aligned}
& F_y=\frac{q E_y}{m} \\
& a_y=2 	imes 10^{11} 	imes 1800 \\
& =36 	imes 10^{13} \mathrm{~m} / \mathrm{s}^2 \\
& 	ext { Time }=\frac{10 	imes 10^{-2}}{v_0}=\frac{0.1}{3 	imes 10^7}=\left(\frac{1}{3} 	imes 10^{-8}ight) \mathrm{sec} 	ext {. } \\
& 	herefore \quad y=\frac{1}{2} a t^2 \\
& \Rightarrow y=\frac{1}{2} 	imes 36 	imes 10^{13} 	imes\left(\frac{1}{3} 	imes 10^{-8}ight)^2 \\
& =2 	imes 10^{-3} \mathrm{~m} \\
& =2 \mathrm{~mm} \\
\end{aligned}
$$

Electrostats & Capacitance

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