The electrostatic potential V at any point (x, y, z) in space is given by `V=4x^(2)`

Options

A. The y- and z-components of the electrostatic field at any point are zero
B. The x-component at any point is given by `(-8xhati)`
C. The x-component at (1, 0, 2) is (-8i)
D. The y- and z-components of the field are constants in magnitude

Explanation

To solve the problem, we need to find the electric field components from the given electrostatic potential \( V = 4x^2 \). The electric field \( \mathbf{E} \) is related to the electrostatic potential \( V \) by the negative gradient of the potential. Let's go through the steps systematically.

### Step 1: Identify the given potential
The electrostatic potential \( V \) is given as:
\[ V = 4x^2 \]

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