The electric field in a region of space is given by $E = 5 i + 2 j N / C$ . Determine the electric flux due to this field through an area $2 m^{2}$ lying in the $Y Z$ plane:

10

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20

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10 \sqrt{2}

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2 \sqrt{29}

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Solution

The correct option is B $10$
Given electric field $E = 5 ˆ i + 2 ˆ j N / C$
area $= 2 m^{2}$ lies in y-z plane. Since area vector is always perpendicular to the surface. So, area $= 2 m^{2} ˆ i$ ; i.e, it lies along the x-axis.
To find flux through the plane:
Since Flux $=$ product of electric field and area vector
So, Flux $= (5 ˆ i + 2 ˆ j) N / C 2 m^{2} ˆ i$
$= (5 \times 2) (ˆ i .^i) N m^{2} / C$
$= 10 N m^{2} / C$

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