☰ Contents · Physics

Self-induction and inductance

Lessons 8 · 1 lessons · N. Sh. Turdiyev, K. A. Tursunmetov, A. G. Ganiyev, K. T. Suyarov, J. E. Usarov, A. K. Avliyoqulov. Physics Grade 11, 1st edition. Niso Poligraf Publishing House, Tashkent, 2018
8

Self-induction. Self-induced EMF. Inductance

Textbook: pp. 29–31
GoalExplain self-induction and calculate with Φ = L·I, Eₛ = –L·ΔI/Δt and the inductance of a solenoid L = μ₀μN²S/l.
New words
self-induction · o‘zinduksiyainductance · induktivlikhenry (H) · genri (H)solenoid · solenoid
Explanation

Self-induction is the appearance of an induced EMF in a circuit itself when the current in it changes, because the circuit's own magnetic flux changes. The flux through the circuit is proportional to the current: Φ = L·I, where L is the inductance, which depends on the size of the circuit, the number of turns and the magnetic properties of the medium. The self-induced EMF is Eₛ = –L·ΔI/Δt: the faster the current changes, the larger the EMF. The unit is the henry (H): 1 H = 1 V·s/A, the inductance of a circuit in which a current changing at 1 A/s induces 1 V. For a long coil (solenoid) of length l, cross-section S and N turns, L = μ₀μN²S/l; a ferromagnetic core multiplies μ, and hence L, many times. Self-induction obeys Lenz's rule: when the circuit is closed the current rises slowly, and when it is opened it falls slowly; inductance gives the current «inertia» in the same way as mass does in mechanics.

Worked examples
The current in a coil of inductance 0.5 H falls uniformly from 4 A to 0 in 0.02 s. |Eₛ| = L·ΔI/Δt = 0.5·4/0.02 = 100 V. This is why sparks appear at the contacts when a circuit with large inductance is opened.
A solenoid has N = 1000, l = 0.5 m, S = 10 cm² = 10⁻³ m², no core (μ = 1). L = μ₀N²S/l = 4π·10⁻⁷·10⁶·10⁻³/0.5 ≈ 2.5·10⁻³ H = 2.5 mH. An iron core (taking μ = 500) would raise L to about 1.26 H.
Class activity

Only with the teacher, using a low-voltage battery and small bulbs: connect two identical bulbs, one in series with an iron-cored coil and one with a resistor, through a switch and see which lights later. Explain which bulb lights slowly using inductance. Connecting a coil to the mains is strictly forbidden.

Practice
1
What is the unit of inductance and how is it defined?
2
L = 40 mH, I = 2.5 A. What is the magnetic flux in mWb?
3
L = 50 mH, the current changes uniformly by 6 A in 0.3 s. What is |Eₛ| in V?
4
Why does a lamp in a circuit with large inductance light up slowly when switched on?