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# Given a Uniform Electric Filed → E = 4 × 10 3 ^ I N / C . Find the Flux of this Field Through a Square of 5 Cm on a Side Whose Plane is Parallel to the Y-z Plane. - Physics

ConceptElectric Flux

#### Question

Given a uniform electric filed $\vec{E} = 4 \times {10}^3 \ \hat{i} N/C$. Find the flux of this field through a square of 5 cm on a side whose plane is parallel to the Y-Z plane. What would be the flux through the same square if the plane makes a 30° angle with the x-axis?

#### Solution

When the plane is parallel to the y-z plane:

$\text { Electric flux }, \phi = \vec{E .} A^\rightharpoonup$

$\text { Here }:$

$\vec{E} = 4 \times {10}^3 \ \hat{i} N/C$

$A^\rightharpoonup = \left( 5 cm \right)^2 \ \hat{i} = 0 . 25 \times {10}^{- 2} \ \hat{i} m^2$

$\therefore \phi = \left( 4 \times {10}^3 \ \hat{i} \right) . \left( 25 \times {10}^{- 4} \ \hat{i} \right)$

$\Rightarrow \phi = 10 \text { Weber }$

When the plane makes a 30° angle with x-axis, the area vector makes a 60° angle with the x-axis.

$\phi = \vec{E .} \vec{A}$

$\Rightarrow \phi = EA \cos\theta$

$\Rightarrow \phi = \left( 4 \times {10}^3 \right)\left( 25 \times {10}^{- 4} \right)\cos60°$

$\Rightarrow \phi = \frac{10}{2}$

$\Rightarrow \phi = 5 \text { Weber }$

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Solution Given a Uniform Electric Filed → E = 4 × 10 3 ^ I N / C . Find the Flux of this Field Through a Square of 5 Cm on a Side Whose Plane is Parallel to the Y-z Plane. Concept: Electric Flux.
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