Worked example: The potential in a region is V(x, y) = (20 V/m²)·(x² − y²)... no — consider the simpler V(x) = (100 V/m)·x, a uniform-field potential. (a) Describe the equipotentials. (b) Find E. (c) How much work to move q = +2 μC from the 30 V surface to the 50 V surface? Step 1: V depends only on x, so surfaces of constant V are planes x = constant, perpendicular to the x-axis, spaced 1 m apart per 100 V. Step 2: E_x = −dV/dx = −100 V/m, so E⃗ = −100·i N/C — uniform, perpendicular to the equipotential planes, pointing from high V toward low V (−x direction). Step 3: W_ext = qΔV = (2 × 10⁻⁶)(50 − 30) = 4 × 10⁻⁵ J. Moving to higher potential costs positive external work for a positive charge. Note the field is strongest nowhere in particular here — equal spacing means uniform E, consistent with |E| = ΔV/Δn = 100/1 = 100 N/C.