Question

The electric field follows the relation
$E = \sqrt{2} r \frac{N}{C}$
where r is distance. Then find the electric flux through cube as given in the image if the sides of the cube are a meter. ​

Answer 1

Given:

The electric field follows the relation

$E = \sqrt{2} r \:N/C$

To find:

Flux through the cube?

Calculation:

Flux at left surface :

$\phi1 = E \times area$

$\implies \phi1 = \{\sqrt{2} (2a) \}\times {a}^{2}$

$\implies \phi1 = 2 \sqrt{2} {a}^{3}$

Flux at right surface:

• At right surface value of r = 2a + a = 3a

$\phi2 = E \times area$

$\implies \phi2 = \{ \sqrt{2} (3a) \} \times {a}^{2}$

$\implies \phi2 = 3 \sqrt{2} {a}^{3}$

Now, net flux will be :

$\phi_{net} = \phi2 - \phi1$

$\implies \phi_{net} = 3 \sqrt{2} {a}^{3} - 2 \sqrt{2} {a}^{3}$

$\implies \phi_{net} = \sqrt{2} {a}^{3}$

So, net flux through cube is √2(a³).