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Standard XII

Physics

Helical Motion

When an beam ...

Question

When an beam consisting of charged particles is projected between the plates of a parallel plate capacitor where an electric field of strength 20 kV/m is applied, the displacement of the particle beam on the screen is 2 cm. If length of plates is 5 cm, distance from centre of plate to the screen is 20 cm and velocity of ions is $10^{6}$ m/s, then q/m of the the charged particle is

10^{6}

C/kg

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10^{7}

C/kg

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10^{8}

C/kg

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10^{1} 1

C/kg

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Solution

The correct option is C $10^{8}$ C/kg
By using $y = \frac{q E L D}{m v^{2}}$ where y = deflection on screen due to electric field only
$\Rightarrow \frac{q}{m} = \frac{y v^{2}}{E L D} = \frac{2 \times 10^{- 2} \times (10^{6})^{2}}{20 \times 10^{3} \times 5 \times 10^{- 2} \times 0.2} = 10^{8} C / k g$ .

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The correct option is C 108 C/kgBy usingy=qELDmv2 where y = deflection on screen due to electric field only ⇒qm=yv2ELD=2×10−2×(106)220×103×5×10−2×0.2=108C/kg.