An LC circuit has zero resistance, no battery, a capacitor C=30microFarads, and

Question

An LC circuit has zero resistance, no battery, a capacitor C=30microFarads, and an inductor L = 0.7 H connected in a simple loop. The capacitor and inductor store a compined total energy of U = 44 microJoules.
(a) If all the circuits energy is stored in the capacitor at time t = 0, when is the soonest time that all the energy will be stored in the inductor?

(b) How much charge is stored on one side of the capacitor at t = 0?

(c) How much current flows through the inductor at the time you found in (a)?

(d) If the inductor is a cylindrical solenoid of length l=4centimeters and radius r=2.8centimeters, find the number of coils in the solenoid.

(e) What is the maximum magnetic field inside the inductor?

(f) If the maximum electric field in the capacitor is E = 1.2 ×103N/C and the space between the plates if filled with a dielectric of constant 100,000, what is the separation between the plates?

(g) What is the area of one of the plates?

Explanation / Answer

a) time required = time period of oscillation/4 = 2pi sqrt(LC) /4 = 0.028/4 sec = 0.007 sec

b) energy stored = 1/2 q^2/C => q = 51.3 microfarad

c) energy stored = 1/2L i^2 => i= 0.011 A

d) L= N^2uA/l where u is premeability of the inner core => N = 3008

e) magnetic field = u N i => B = 4.1 * 10^(-5) T

now I will solve g first

g) E = q^2/Ae where e is the permittivity of the material inside ( here permittivity of free space * 100000)=> A = 2.4 * 10^-6) m^2

f) C = eA/d => d = 7* 10^(-8) m.

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