[Case Study] The figure shows four pairs of parallel identical cond...

Question

[Case Study] The figure shows four pairs of parallel identical conducting plates (Sets I, II, III, IV), separated by the same distance 2.0 cm, arranged perpendicular to the x-axis. The electric potential of each plate is given: Set I: −70V, −50V. Set II: −50V, +150V. Set III: −20V, +200V. Set IV: −100V, −400V. The electric field between each pair is uniform and normal to the plates.

(i) For which pair of plates is the electric field $\vec E$ along $\hat i$?

Accepted Answer

Step 1: Electric field points from HIGH potential to LOW potential, i.e., in the direction of DECREASING potential.

Step 2: Field is along $+\hat i$ (i.e. left-to-right, in the direction of increasing x, matching the plate order shown left-to-right) only if potential decreases from left plate to right plate.

Step 3: Checking each set (left plate value → right plate value): Set I: −70→−50 (increasing, so field is along $-\hat i$). Set II: −50→+150 (increasing, field along $-\hat i$). Set III: −20→+200 (increasing, field along $-\hat i$). Set IV: −100→−400 (DECREASING, so field is along $+\hat i$).

Step 4: Answer: (D) IV.

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