**Question:**Which of the following electrostatic fields could exist in a finite region of space that contains no charges? (In these expressions, A is a constant, i, j, and k are unit vectors pointing in the x, y, and z direction, respectively.)a. \( A (2xy \, \mathbf{i} - x \, \mathbf{k}) \)b. \( A (xz \, \mathbf{i} + xz \, \mathbf{j}) \)c. \( A xyz (\mathbf{i} + \mathbf{j}) \)d. \( A (-y \, \mathbf{j} + z \, \mathbf{k}) \)e. \( A xyz \, \mathbf{i} \)**Answer Options:**- ☐ d- ☑ a- ☐ b- ☐ c**Explanation:**The correct answer is option **a**: \( A (2xy \, \mathbf{i} - x \, \mathbf{k}) \). This field could exist in a finite region without charges because its curl is zero, satisfying the condition for an electrostatic field in a charge-free region.

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