Two flat 4.0 cm × 4.0 cm electrodes carrying equal but opposite charges are spaced 2.0 mm apart with their midpoints opposite each other. Between the electrodes but not near their edges, the electric field strength is 2.5 × 10⁶ N/C. What is the magnitude of the charge on each electrode? (ε0 = 8.85 × 10^-12 C²/N ∙ m²)

Question

Quizplus · Accepted Answer

The electric field strength between two flat parallel plates is given by:E = σ / ε0where σ is the surface charge density and ε0 is the permittivity of free space.In this problem, we are given the electric field strength E = 2.5 × 106 N/C, the distance between the plates d = 2.0 mm = 0.002 m, and the area of each plate A = (0.04 m)2 = 0.0016 m2.We can solve for the surface charge density σ:σ = Eε0 = (2.5 × 106 N/C)(8.85 × 10-12 C2/N ∙ m2) = 2.21 × 10-5 C/m2The total charge on each electrode is then:Q = σA = (2.21 × 10-5 C/m2)(0.0016 m2) = 35 nCTherefore, the magnitude of the charge on each electrode is 35 nC.

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