In a region of space the electric field in the `x`-direction and proportional to `x`i.e., `vec(E )=E_(0)xhat(i)`. Consider an imaginary cubical volume of edge a with its parallel to the axes of coordinates. The charge inside this volume will be

Explanation

To find the charge inside a cubical volume in an electric field defined by \(\vec{E} = E_0 x \hat{i}\), we can use Gauss's law. Here are the steps to solve the problem:

### Step 1: Understand the Electric Field
The electric field is given as \(\vec{E} = E_0 x \hat{i}\), which means the electric field varies linearly with the \(x\)-coordinate. At any point \(x\), the electric field has a magnitude of \(E_0 x\) and points in the positive \(x\) direction.

### Step 2: Define the Cubical Volume
Consider a cube with edge length \(a\), positioned such that one of its corners is at the origin \((0, 0, 0)\) and the opposite corner is at \((a, a, a)\). The cube's faces are parallel to the coordinate axes.

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