The electric field in a region of space near the origin is given by\[\mathbf{E}(x, y, z) = E_0 \left( \frac{y \hat{\mathbf{i}} + x \hat{\mathbf{j}}}{a} \right)\](a) Evaluate the curl \(\nabla \times \mathbf{E}(x, y, z)\).(b) Setting \(V(0, 0, 0) = 0\), select a path from \((0, 0, 0)\) to \((x, y, 0)\) and compute \(V(x, y, 0)\).(c) Sketch the four distinct equipotential lines that pass through the four points \((a, a)\), \((-a, a)\), \((-a, -a)\), and \((a, -a)\). Label each line by the value of \(V\).**Graph/Diagram Explanation**: The bottom right of the image contains an empty grid. This grid is likely intended for sketching the equipotential lines as requested in part (c) of the problem. The grid would help in accurately plotting the lines through specified coordinates.

(a) Curl is, ∇×E=i^j^k^∂∂x∂∂y∂∂zE0yaE0xa0=E0a-E0ak^=0

Answered: The electric field in a region of space…

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