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  4. The electric field in a region of space is given by, vecE = Eo hati + 2 Eo hatj where E0 = 100 N/C. The flux of this field through a circular surface of radius 0.02 m parallel to the Y-Z plane is nearly :

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Q. The electric field in a region of space is given by, $\vec{E} = E_{o} \hat{i} + 2 E_{o} \hat{j}$ where $E_{0} = 100\, N/C$. The flux of this field through a circular surface of radius $0.02\, m$ parallel to the $Y-Z$ plane is nearly :

JEE MainJEE Main 2014Electric Charges and Fields

Solution:

$\phi =\left( E _{0} \hat{ i }+2 E _{0} \hat{ j }\right) \cdot\left(\pi R ^{2}\right) \hat{ i }$
$\phi =100 \times \pi \times(0.02)^{2} $
$=0.125$