Electric Field and Charge Particle in Electric Field

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Q 21 :

As shown in the figure, a configuration of two equal point charges ( $q_{0} = + 2 μ C$ ) is placed on an inclined plane. The mass of each point charge is 20 g. Assume that there is no friction between the charge and the plane. For the system of two point charges to be in equilibrium (at rest), the height $h = x \times 10^{- 3} m .$ The value of $x$ is ______.

(Take $\frac{1}{4 π ε_{0}} = 9 \times 10^{9} {N m}^{2} C^{- 2},$ $g = 10 {ms}^{- 1}$ ) [2023]

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(300)

$For equilibrium along the plane$

$m g \sin θ = \frac{1}{4 π ε_{0}} \times \frac{q_{0}^{2}}{{(h \cos e c 30 °)}^{2}}$

$∴$ $h^{2} = \frac{1}{4 π ε_{0}} \times \frac{q_{0}^{2}}{m g cosec 30 °} = 9 \times 10^{9} \times \frac{{(2 \times 10^{- 6})}^{2}}{0.02 \times 10 \times 2}$

$∴$ $h = 3 \times 10^{4} \times \frac{2 \times 10^{- 6}}{2} = 0.3 m = 300 mm$

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