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Introductory Physics Homework Help
Force needed to hold together a capacitor
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[QUOTE="phantomvommand, post: 6465411, member: 687416"] [B]Homework Statement:[/B] The inner surfaces of 2 *insulating* plates are given a charge Q. What is the force required to hold them together? [B]Relevant Equations:[/B] F = 1/2 (E outside + E inside) * Q I have 2 methods, which give 2 different solutions: Let sigma = charge per unit area Let plate 1 be the left plate, plate 2 = right plate. Method 1: Because they are insulating, consider the electric field at 3 regions; region 1 to the left of plate 1, region 2 between the plates, and region 3 to the right of plate 2. Because the plates are insulating, Electric field in the regions are superpositions of the field due to each plate. Region 1 has field = sigma/e0 + 0 = [B]sigma/e0 directed leftwards[/B], Region 2 has field = sigma/e0 - sigma/e0 = [B]0[/B], Region 1 has field = sigma/e0 + 0 = [B]sigma/e0 directed rightwards[/B], Average force on plate 1 = sigma/2e0 *Q (Average E field * Q)= Asigma^2/2e0 = Q^2/2Ae0, where A is area of plate. (force directed leftwards) Similarly, force on plate 2 = Q^2/2Ae0. (force directed rightwards) Thus, total force needed to hold the plates together is Q^2/Ae0. Method 2: Consider the capacitance of the system. C = e0A/x, where x is plate separation. Energy = Q^2x/2Ae0. F = dE/dx = Q^2/2A e0. Method 2 gives the correct answer. Why is method 1 wrong? [/QUOTE]
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Force needed to hold together a capacitor
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