The electric field in a region is given by `E = (4 axy sqrt(z))hat i + (2 ax^2 sqrt(z)) hat j + (ax^2 y// sqrt(z)) hat k`
where A is a positive constant. The equation of an equipotential surface will be of the form.

Explanation

To find the equation of an equipotential surface given the electric field \( \mathbf{E} = (4 axy \sqrt{z}) \hat{i} + (2 ax^2 \sqrt{z}) \hat{j} + \left(\frac{ax^2 y}{\sqrt{z}}\right) \hat{k} \), we can follow these steps:

### Step 1: Understand the relationship between electric field and electric potential
The electric field \( \mathbf{E} \) is related to the electric potential \( V \) by the equation:
\[ \mathbf{E} = -\nabla V \]
This implies that the change in potential \( dV \) can be expressed as:
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