Instantaneous energy of magnetic field¶

There is an oscillatory circuit with alternating current. Then the energy of the magnetic field in the inductor will depend on the inductance, the maximum value of the current, the angular frequency of the current, the time and the initial phase.

Conditions:

The current depends on time sinusoidally:

\[I(t) = I_\text{max} \cos(\omega t + \varphi)\]

energy¶: energy stored in the coil.

Symbol:: E
Latex:: \(E\)
Dimension:: energy

inductance¶: inductance of the coil.

Symbol:: L
Latex:: \(L\)
Dimension:: inductance

current_amplitude¶: current amplitude.

Symbol:: I_max
Latex:: \(I_\text{max}\)
Dimension:: current

angular_frequency¶: angular_frequency of the current.

Symbol:: w
Latex:: \(\omega\)
Dimension:: angle/time

time¶: time.

Symbol:: t
Latex:: \(t\)
Dimension:: time

initial_phase¶: Initial phase_shift of the oscillations.

Symbol:: phi
Latex:: \(\varphi\)
Dimension:: angle

law¶

E = L * I_max^2 / 2 * cos(w * t + phi)^2

Latex:: \[E = \frac{L I_\text{max}^{2}}{2} \cos^{2}{\left(\omega t + \varphi \right)}\]