Self and Mutual Inductance
Inductance of a solenoid and energy stored in a magnetic field. (Physics › Electromagnetic Induction and Alternating Currents, NEET UG syllabus.)
What is Self and Mutual Inductance?
The property of a coil to oppose any change in the current flowing through it by inducing an EMF in itself.
Key formula / rule: Magnetic Flux (Self-induction)
Key points
- Define self-inductance and mutual inductance.
- Derive and apply expressions for self-inductance of a solenoid.
- Understand and calculate the energy stored in an inductor's magnetic field.
- Differentiate between self-induction and mutual induction.
Common exam trap
Confusing self-inductance with mutual inductance.
Definitions
- Term
Self-inductance
- Meaning
The property of a coil to oppose any change in the current flowing through it by inducing an EMF in itself.
- Term
Mutual Inductance
- Meaning
The property of two coils by virtue of which a changing current in one coil induces an EMF in the other coil.
- Term
Henry (H)
- Meaning
The SI unit of inductance. One Henry is the inductance of a coil in which an EMF of one volt is induced when the current in the coil changes at the rate of one ampere per second.
Learning objectives
Define self-inductance and mutual inductance.
Derive and apply expressions for self-inductance of a solenoid.
Understand and calculate the energy stored in an inductor's magnetic field.
Differentiate between self-induction and mutual induction.
Solve problems involving self-inductance, mutual inductance, and energy storage.
Formulae
- Name
Magnetic Flux (Self-induction)
- Note
Magnetic flux linked with a coil due to its own current.
- Expression
Φ = LI
- Name
Self-induced EMF
- Note
L is self-inductance, dI/dt is the rate of change of current.
- Expression
ε = -L (dI/dt)
- Name
Self-inductance of a long solenoid
- Note
N = total turns, A = cross-sectional area, l = length. (Alternatively, L = μ₀n²Al, where n=N/l is turns per unit length).
- Expression
L = (μ₀N²A)/l
- Name
Magnetic Flux (Mutual induction)
- Note
Flux linked with secondary coil due to current in primary coil.
- Expression
Φ₂ = MI₁
- Name
Mutually induced EMF
- Note
M is mutual inductance, dI₁/dt is rate of change of current in primary coil.
- Expression
ε₂ = -M (dI₁/dt)
- Name
Mutual inductance of two long coaxial solenoids
- Note
N₁, N₂ = turns of primary and secondary, A = common cross-sectional area, l = common length.
- Expression
M = (μ₀N₁N₂A)/l
- Name
Energy stored in an inductor
- Note
L is self-inductance, I is the current flowing through the inductor.
- Expression
U = (1/2)LI²
- Name
Energy density in a magnetic field
- Note
B is the magnetic field strength, μ₀ is the permeability of free space.
- Expression
uB = B²/(2μ₀)
Prerequisites
Faraday's Law of Electromagnetic Induction
Lenz's Law
Magnetic flux
Magnetic field due to a solenoid
Basic calculus (derivatives)
Common mistakes
Confusing self-inductance with mutual inductance.
Incorrectly applying Lenz's Law to determine the direction of induced EMF.
Forgetting the negative sign in the induced EMF formulae (ε = -L dI/dt or ε = -M dI₁/dt).
Assuming inductance depends on the current flowing through the coil.
Using incorrect formulae for the inductance of a solenoid or energy stored.
Keywords
Self-inductance
Mutual inductance
Inductor
Magnetic flux
Induced EMF
Lenz's Law
Solenoid
Energy storage
Henry
Magnetic field energy density
Electromagnetic Induction
Practice preview
What is the SI unit of self-inductance?…
easy
The energy stored in an inductor carrying a current I is given by the formula:…
easy
A coil has a self-inductance of 10 mH. If the current in the coil changes from 5 A to 2 A in 0.1 seconds, what is the magnitude of the average induced EMF, and what is the change in energy stored in the coil?…
hard