<h2>
Answer:</h2>
The equation of the electric field (E) is given by;
E = -1000x
<h2>
Explanation:</h2>
The electric field (E) is the gradient of the potential difference (V) in the direction of x between two points. i.e
E =
----------------------(i)
From the question;
V = ax² + b ---------------(ii)
Find the gradient of equation (ii) by taking derivative of both sides with respect to x as follows;
= 
= 2ax ----------------------(iii)
Substitute
= 2ax into equation (i) as follows;
E = 2ax --------------------------(iv)
Now, substitute the value of a = -500 into equation (iv) as follows;
E = 2(-500)x
E = -1000x
Therefore, the equation of the electric field (E) is given by;
E = -1000x