A surface with area \( \vec{S} = 20\hat{k} \) is held in an electric field \( \vec{E} = \hat{\imath} + 2\hat{\jmath} + 5\hat{k} \). The electric flux linked with the surface is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 100 units
The electric flux through a flat surface in a uniform field is the dot product of the field and the area vector.
\( \displaystyle \phi = \vec{E}\cdot\vec{S} = (\hat{\imath} + 2\hat{\jmath} + 5\hat{k})\cdot(20\hat{k}) \)
Only the \( \hat{k} \) components multiply, since \( \hat{\imath}\cdot\hat{k} = \hat{\jmath}\cdot\hat{k} = 0 \).
\( \displaystyle \phi = 5 \times 20 = 100\ \text{units} \)