A stream of a positively charged particles having q m = 2 × 10 11 C kg - 1 and velocity v → 0 = 3 × 10 7 i ^ m s - 1 is deflected by an electric field 1 . 8 j ^ kV m - 1 . The electric field exists in

Question

A stream of a positively charged particles having q m = 2 × 10 11 C kg - 1 and velocity v → 0 = 3 × 10 7 i ^ m s - 1 is deflected by an electric field 1 . 8 j ^ kV m - 1 . 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 .

TestHub · Accepted Answer

Acceleration of the particles due to electric field, $a = \frac{F}{m} = \frac{q E}{m} = (2 \times 10^{11}) (1.8 \times 10^{3})$

$= 3.6 \times 10^{14} m s^{- 2}$

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

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

Now deflection,

$y = \frac{1}{2} {at}^{2} = \frac{1}{2} (3.6 \times 10^{14}) {(\frac{0.10}{3 \times 10^{7}})}^{2}$

$= 0.002 m$

$= 2 mm$

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