First slide

Electric Flux

Question

In a region, electric field depends on X-axis as E = E₀x². There is a cube of edge a as shown. Then find the charge enclosed in that cube.

Moderate

A

5 $ε$ ₀ a⁴ E₀
B

3 $ε$ ₀ a⁴ E₀
C

4 $ε$ ₀ a⁴ E₀
D

Zero

Solution

E = E₀x² ; Electric field varies from 2a to 3a
Hence ${[E_{0} x^{2}]}_{2 a}^{3 a} ds = \frac{q}{ε_{0}}$
$[E_{0} {(3 a)}^{2} - E_{0} {(2 a)}^{2}] . a^{2} = \frac{q}{ε_{0}} 5 a^{4} E_{0} = \frac{q}{ε_{0}} \Rightarrow q = 5 ε_{0} a^{4} E_{0}$

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