A capacitor is constructed from two square, metallic plates of sides ? and separ

Question

A capacitor is constructed from two square, metallic plates of sides ? 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, ?, ?, Q, d, and x.)

(a) Find the equivalent capacitance of the device.

(b) Calculate the energy stored in the capacitor.

(c) Find the direction and magnitude of the force exerted by the plates on the dielectric.

(d) Obtain a numerical value for the force when x = ?/2, assuming ? = 5.10 cm, d = 1.90 mm, the dielectric is glass (? = 4.50), and the capacitor was charged to 1.90 103 V before the dielectric was inserted.

Explanation / Answer

A. Equivalent Capaciance Ceq = {(K-1)x/l + 1} eo l^2/d
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B. Net Energy Stored U = 0.5 Ceq dV^2

U = (0.5 * eo L^2 dV^2/d) * (x(k-1)/l + 1)

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C.

Force Vector F = dU/dt

F = eo L(K-1) dV^2 /2d

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d. F = 8.85 e -12 * 0.051 *(4.5-1) * 1900*1900/(2 * 1.9 e -3)

F = 1500.74 u N

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