A capacitor is constructed from two square, metallic plates of sides ℓ and separation d. Charges +Q and -Q are placed on the plates, and the power supply is then removed. A material of dielectric constant ? is inserted a distance x into the capacitor as shown in the figure below. Assume d is much smaller than x. Suggestion: The system can be considered as two capacitors connected in parallel. (Use the following as necessary: ?0, ?, ℓ, Q, d, and x.)(a) Find the equivalent capacitance of the device.Ceq = (b) Calculate the energy stored in the capacitor.U = (c) Find the direction and magnitude of the force exerted by the plates on the dielectric.magnitude direction (d) Obtain a numerical value for the force when x = ℓ/2, assuming ℓ = 4.60 cm, d = 1.90 mm, the dielectric is glass (? = 4.50), and the capacitor was charged to 2.20 103 V before the dielectric was inserted.magnitude µNdirection

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College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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A capacitor is constructed from two square, metallic plates of sides ℓ and separation d. Charges +Q and -Q are placed on the plates, and the power supply is then removed. A material of dielectric constant ? is inserted a distance x into the capacitor as shown in the figure below. Assume d is much smaller than x. Suggestion: The system can be considered as two capacitors connected in parallel. (Use the following as necessary: ?₀, ?, ℓ, Q, d, and x.)

(a) Find the equivalent capacitance of the device.
C_eq =

(b) Calculate the energy stored in the capacitor.

U =

magnitude
direction

(d) Obtain a numerical value for the force when x = ℓ/2, assuming ℓ = 4.60 cm, d = 1.90 mm, the dielectric is glass (? = 4.50), and the capacitor was charged to 2.20 10³ V before the dielectric was inserted.