Answer: E = (0, -(b/(a^2+y^2)))
Step-by-step explanation:
The electric field is given by the negative gradient of the electric potential: E = -∇V.
In this case, the electric potential V is a function of y only, so the electric field will only have a y-component. The y-component of the electric field can be calculated using the gradient:
Ey = -(∂V/∂y)
= -(b/(a^2+y^2))
The x-component of the electric field is zero because the electric potential does not depend on x.
Therefore, the electric field is given by:
E = (0, Ey)
= (0, -(b/(a^2+y^2)))