Faraday's law and Lenz's law; self and mutual inductance; factors affecting the inductance of a coil; the L-R time constant and energy stored in a magnetic field.
Notes
Inductance — summary notes
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Main ideas
Faraday's law: the EMF induced in a coil is proportional to the rate of change of flux linkage — EMF = −N·dΦ/dt.
Lenz's law is the minus sign: the induced EMF always opposes the change that produced it.
Self-inductance L is measured in henries. The EMF induced by a changing current in the same coil is EMF = −L·di/dt.
Inductance rises with the SQUARE of the number of turns, with core permeability and with cross-sectional area, and falls with length.
Energy stored in the magnetic field is E = ½LI².
The L-R time constant is τ = L / R. Current rises to 63.2% of its final value in one time constant.
⚠ Exam trap: Lenz means opposition, and because L ∝ N², doubling the turns roughly quadruples the inductance — not doubles it.
Key formulas
Faraday's law
EMF = −N · dΦ/dt
Self-induced EMF
EMF = −L · di/dt
Inductance of a coil
L = μN²A / l (L ∝ N²)
Energy stored
E = ½LI²
Time constant
τ = L / R
Solved examples
A coil of 200 turns has an inductance of 4 H. Roughly what inductance results from rewinding it with 400 turns on the same core?
L ∝ N². Doubling the turns multiplies L by 2² = 4, giving approximately 16 H.
A 2 H inductor carries 3 A. Find the energy stored in its magnetic field.