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Q.

In the figure shown, there is a large sheet of charge of uniform surface charge density $σ$ . A charge particle of charge -q and mass m is projected from a point A on the sheet with a speed u with angle of projection such that it lands at maximum distance from A on the sheet. Neglecting gravity, find the time of flight.

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a

$\frac{2 \sqrt{2} {mvε}_{0}}{σq}$

b

$\frac{\sqrt{2} {mvε}_{0}}{5 σq}$

c

$\frac{{mvε}_{0}}{\sqrt{2} σq}$

d

$\frac{{mvε}_{0}}{2 \sqrt{2} σq}$

answer is A.

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Detailed Solution

For maximum distance angle of projection should be 45°.

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$For vertical displacement, \vec{S} = \vec{u} t + \frac{1}{2} \vec{a} t^{2} 0 = usin 45^{\circ} t + \frac{1}{2} \cdot \frac{q \cdot \frac{σ}{2 ε_{0}}}{m} t^{2} \Rightarrow t = 0 or t = \frac{2 \sqrt{2} {mvε}_{0}}{σq} \Rightarrow time of flight = \frac{2 \sqrt{2} {mvε}_{0}}{σq}$

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In the figure shown, there is a large sheet of charge of uniform surface charge density σ. A charge particle of charge -q and mass m is projected from a point A on the sheet with a speed u with angle of projection such that it lands at maximum distance from A on the sheet. Neglecting gravity, find the time of flight.