Explanation:

In electromagnetism, the curl of a vector field represents the rotation or circulation of that field. The curl of a vector field E is denoted as ∇ × E.

Definition of Irrotational:
A vector field is said to be irrotational if its curl is zero (∇ × E = 0). This means that there is no rotation or circulation in the field.

Static Fields:
Static fields are those in which the electric and magnetic fields do not vary with time. In other words, the fields are constant and not changing over time.

The Curl of E in Static Fields:
When dealing with static fields, the time derivatives in Maxwell's equations become zero. Therefore, the curl of the electric field (∇ × E) in static fields is also zero.

Interpretation:
If the curl of E is zero (∇ × E = 0), it means that the electric field is irrotational. This implies that there is no rotation or circulation of the electric field in static situations.

Conclusion:
Therefore, for static fields, the curl of E will be irrotational (option B). The absence of rotation or circulation in the electric field indicates that the field is not changing or rotating around any axis. It remains constant and is not diverging or converging towards or away from any point or region.

In summary:
- Static fields have no time variation.
- The curl of a vector field represents rotation or circulation.
- In static fields, the curl of E is zero (∇ × E = 0).
- A vector field with zero curl is called irrotational.
- Therefore, for static fields, the curl of E is irrotational.