In the oscillatory circuit, the electric charge of the capacitor changes according to the law Q = 10 ^ -4 cos

In the oscillatory circuit, the electric charge of the capacitor changes according to the law Q = 10 ^ -4 cos (10 ^ 4 πt). Determine the law of change in the current strength in the circuit: the maximum energy of the electric and magnetic fields in the circuit; loop inductance. The capacitance of the capacitor is 100 pF.

First, we calculate Qm using the following formula:
Qm = 10 ^ -4 * i (t) = – 10 ^ -4 * 10 ^ 4 * pi * sin 10 ^ 4 * p i * t = – pi * sin10 ^ 4 * pi * t;
Now let’s count Im:
Im = 10 ^ -4 * 10 ^ 4 * pi A = 3.14 A;
Next, we find Ee:
Ee = Em = Qm ^ 2/2 * C = 10 ^ -8 / 2 * 100 * 10 ^ -9 = 0.05 J;
Now let’s use the formula:
Em = L * Im ^ 2/2;
Let’s transform:
L = 2 * Em / I ^ 2;
Let’s substitute:
L = 2 * 0.05 / 3.14 ^ 2;
L = 0.01 H.
Answer: L = 0.01 H.