Question

A capacitor is constructed from 2 square, metallic plates of side’s scripted l and separation d. Charges +Q and -Q are placed on plates, and the power provide is then removed. A material of dielectric constant κ is inserted a distance x into capacitor. Imagine d is much smaller than x.

Determine the energy stored in the capacitor. (Use epsilon_0 for ε0, kappa for κ, l for scripted l, Q, d, and x, as necessary.)

Find out direction and magnitude of force exerted by the plates on the dielectric. (Use epsilon_0 for ε0, kappa for κ, l for scripted l, Q, d, and x, as necessary.)

Obtain a numerical value for force when x = scripted l / 2, assume scripted l = 5.40 cm, d = 2.10 mm, the dielectric is glass (κ = 4.5), and the capacitor was charged to 2000 V before dielectric was inserted.