Two parallel circular plates with radius 7.0 mm carrying equal-magnitude surface charge densities of ±3.0 μC/m² are separated by a distance of 1.0 mm.How much stored energy do the plates have?

Question

Quizplus · Accepted Answer

The stored energy is given by U = (1/2)CV^2, where C is the capacitance of the plates and V is the potential difference between them. The capacitance of two parallel plates is given by C = εA/d, where ε is the permittivity of the vacuum, A is the area of the plates, and d is the distance between them. The potential difference between the plates is given by V = Ed, where E is the electric field between the plates. The electric field between two parallel plates is given by E = σ/ε, where σ is the surface charge density. Substituting these expressions into the equation for stored energy, we get:U = (1/2)(εA/d)(Ed)^2 = (1/2)εA(σ^2/ε) = (1/2)σ^2APlugging in the given values, we get:U = (1/2)(3.0 μC/m^2)^2(π(7.0 mm)^2) = 78 nJ

Two Parallel Circular Plates with Radius 7