A stream of positively charged particles having and velocity deflected by an electric field The electric field exists in a region of 10 cm along the -direction. [2023]

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Solution

Q.
A stream of positively charged particles having $\frac{q}{m} = 2 \times 10^{11} \frac{C}{kg}$ and velocity ${\vec{v}}_{0} = 3 \times 10^{7} \hat{i} m/s$ deflected by an electric field $1.8 \hat{j} kV/m .$ The electric field exists in a region of 10 cm along the $x$ -direction. Due to the electric field, the deflection of the charged particles in the $y$ -direction is ________ mm. [2023]

Ans.
(2)

$a = \frac{F}{m} = \frac{q E}{m} = (2 \times 10^{11}) (1.8 \times 10^{3}) = 3.6 \times 10^{14} {m/s}^{2}$

$Time to cross plates t = \frac{d}{v}$

$t = \frac{0.10}{3 \times 10^{7}}$

$y = \frac{1}{2} a t^{2} = \frac{1}{2} (3.6 \times 10^{14}) {(\frac{0.01}{9 \times 10^{14}})}^{2}$

$= 0.2 \times 0.01 = 0.002 m = 2 mm$

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