Assume that an electric field E=30x²î exists in space. Then the potential difference VA−VO, where VO is the potential at the origin and VA the potential at x=2m is :

The electric field is given by E = 30x²î. The potential difference between two points A and B is given by the line integral of the electric field:

ΔV = -∫E⋅dl

Since the electric field is only in the x-direction, and the path is along the x-axis, the dot product simplifies to:

ΔV = -∫Ex dx

In this case, Ex = 30x², so:

ΔV = -∫(30x²)dx from x=0 to x=2

Integrating, we get:

ΔV = -[10x³] from x=0 to x=2

ΔV = -[10(2)³ - 10(0)³] = -80 V

Since VA - VO = -80V, the potential difference is -80V. However, the question asks for the magnitude of the potential difference. Therefore, the potential difference is 80V.

Therefore, the correct answer is 80V.