Self Inductance, Mutual Inductance, and Energy Stored

Identify whether one coil or two coils are involved. Check whether current changes with time. Use L for same-coil induction and M for coupled coils. Calculate rate of change of current, then apply the emf formula with units. Use Lenz's law for sign or direction.

For self induction, show one coil with changing current and back emf. For mutual induction, show two nearby coils labelled primary and secondary, with changing current in the primary and induced emf in the secondary.

Applying epsilon = -L dI/dt when current is constant, or writing energy as LI^2 instead of 1/2 LI^2.

Self inductance is the property of a coil by which a changing current in it induces an emf in the same coil. Mutual inductance is the property by which a changing current in one coil induces an emf in a nearby coil.

Self inductance is the property of a coil by which a changing current in it induces an emf in the same coil. Mutual inductance is the property by which a changing current in one coil induces an emf in a nearby coil. Self induction: epsilon = -L dI/dt, where L is self inductance in henry, I is current in ampere, t is time in second, and epsilon is volt. Mutual induction: epsilon_2 = -M dI_1/dt, where M is mutual inductance in henry. Energy stored in an inductor: U = 1/2 L I^2 in joule. Use these when current changes with time, not for steady DC after transients settle. When current through an inductor is increased suddenly, the inductor opposes the rise of current by producing back emf. In a transformer-like pair of coils, changing current in one coil can induce emf in the other due to mutual inductance.

In self induction, the coil's own changing current changes magnetic flux linked with it, producing back emf epsilon = -L dI/dt. In mutual induction, changing current in the primary coil changes flux linked with the secondary coil, producing induced emf epsilon = -M dI/dt. An inductor stores magnetic energy U = 1/2 L I^2. Self induction: epsilon = -L dI/dt, where L is self inductance in henry, I is current in ampere, t is time in second, and epsilon is volt. Mutual induction: epsilon_2 = -M dI_1/dt, where M is mutual inductance in henry. Energy stored in an inductor: U = 1/2 L I^2 in joule. Use these when current changes with time, not for steady DC after transients settle. An inductor of 0.80 H carries current increasing uniformly from 1.0 A to 3.0 A in 0.20 s. Magnitude of induced emf = L Delta I/Delta t = 0.80 x (2.0/0.20) = 8.0 V. Energy stored at 3.0 A is U = 1/2 L I^2 = 0.5 x 0.80 x 9.0 = 3.6 J. The induced emf opposes the increase of current. Questions may ask definitions, SI unit henry, back emf reasoning, energy stored in an inductor, or comparison between self and mutual induction. Applying epsilon = -L dI/dt when current is constant, or writing energy as LI^2 instead of 1/2 LI^2.