I have the electric field in a region give by:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\vec E = \frac{k}{\epsilon_0 a^4} \left(ax^2\hat x + yz^2\hat y + y^2z\hat z\right)[/tex]

where 'k' and 'a' are constants.

There are few questions I need to solve.

1: Is the field conservative?

A: Yes. I computed the curl and found it equal to zero.

[tex]\nabla \times \vec E = 0[/tex]

2: Calculate the charge density at a point P(x,y,z).

A: I applied the differential form of Gauss's law.

[tex]\nabla \cdot \vec E = \frac{\rho}{\epsilon_0}[/tex]

[itex]\rho[/itex] is the charge density.

So, I got the charge density as:

[tex]\rho = \epsilon_0 \left[2ax + y^2 + z^2\right][/tex]

Please verify if my method is correct.

3: Determine the charge enclosed in a cube of side 'a' with one of its corners at the origin and sides parallel to x,y and z axes.

A: I applied Gauss's law here too!

[tex]\int \vec E \cdot d\vec a = \frac{Q_{enclosed}}{\epsilon_0}[/tex]

How do I calculate the flux here?

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# Homework Help: Problem on electric field

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