A uniform electric field $a^i + b^j$ intersects a surface of area A. What is the flux through this area if the the surface lies (a) in the yz plane, (b) in the xz plane, (c) in the xy plane?

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Solution

$\to E = a^i + b^j$
(a) $\to A = A^i \Rightarrow ϕ = \to E . \to A = A a$
(b) $\to A = A^j \Rightarrow ϕ = \to E . \to A = A b$
(c) $\to A = A^k \Rightarrow ϕ = \to E . \to A = 0$

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