A particle that carries a charge ‘-q’ is placed at rest in uniform electric field 10N/C. It experiences a force and moves. In a certain time ‘t’, it is observed to acquire a velocity $10 \hat{i} - 10 \hat{J} m / s$ . The given electric filed intersects a surface of area 1m² in the x-z plane. Find the electric flux through the surface.

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$10 \sqrt{3} {Nm}^{2} / C$

$5 \sqrt{3} {Nm}^{2} / C$

$5 \sqrt{2} {Nm}^{2} / C$

$10 \sqrt{2} {Nm}^{2} / C$

answer is A.

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Detailed Solution

Force on charge $F = q E$

$∴$ particle moves opposite to $E$ with $V$

Unit vector in the direction of $V$ is $\frac{i}{\sqrt{2}} - \frac{j}{\sqrt{2}}$

Unit vector in the direction of $E$ is $- \frac{i}{\sqrt{2}} + \frac{j}{\sqrt{2}}$

$\bar{E} = 10 [\frac{- i}{\sqrt{2}} + \frac{j}{\sqrt{2}}] and \bar{A} = 1 \times \bar{j}$

Electric flux $Φ = \bar{E} \cdot \bar{A} = 5 \sqrt{2} {Nm}^{2} / C$

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