In a coil with an inductance of 20 mH, the current is 0.5 A. How much will the energy of the magnetic field increase

In a coil with an inductance of 20 mH, the current is 0.5 A. How much will the energy of the magnetic field increase if an iron core is inserted into the coil, which will increase the inductance of the coil by 50 times? the current in the circuit does not change.

L1 = 50 (mH) = 50 * 10 ^ -3 (H)
I = 0.5 (A)

Energy formula:
W = (LI ^ 2) / 2

Let’s compare the energies before and after the increase:
W1 = (L * I ^ 2) / 2 = (20 * 10 ^ -3 * 0.5 ^ 2) / 2 = 1/200 = 2.5 * 10 ^ -3
W2 = (50L * I ^ 2) / 2 = (20 * 10 ^ -3 * 0.5 ^ 2 * 50) / 2 = 1/8 = 0.125 * 10 ^ -3

ΔW = W1 – W2 = 0.125 * 10 ^ 3 – 2.5 * 10 ^ -3 – = 2.375 * 10 ^ 3

Answer: ΔW = 2.375 * 10 ^ 3