Key Points in Electromagnetic Induction
1 Fundamentals and Magnetic Flux
1.1 Definition of Electromagnetic Induction (EMI)
Electromagnetic Induction is the process by which a changing magnetic field through a
conductor or a coil induces an electric current (and thus an Electromotive Force, or EMF)
in that conductor. This phenomenon, discovered by Michael Faraday in 1831, forms the
basis for nearly all modern electrical power generation.
1.2 Magnetic Flux (ΦB )
Magnetic flux is a measure of the total number of magnetic field lines passing through a
given area. A change in this quantity is the necessary condition for EMI.
The magnetic flux ΦB through an area A in a uniform magnetic field B ~ is defined as:
~ ·A
ΦB = B ~ = BA cos θ
~ and the area vector (A).
where θ is the angle between the magnetic field vector (B) ~
• Unit: The SI unit of magnetic flux is the weber (Wb), where 1 Wb = 1 Tesla · meter2
(1 T · m2 ).
• Change in Flux: Magnetic flux can change in three ways: (1) Changing the magni-
tude of B,~ (2) Changing the area A exposed to B,
~ or (3) Changing the angle θ.
1.3 Faraday’s Law of Induction
Faraday’s Law quantitatively describes the magnitude of the induced EMF (E) in a circuit.
It states that the induced EMF in a coil is directly proportional to the rate of change of
magnetic flux through the coil.
For a coil with N turns, the induced EMF is:
dΦB
E = −N
dt
• The unit of EMF is the volt (V).
• If the induced current I flows through a resistance R, the current is I = E/R.
1.4 Lenz’s Law (Direction of Induced Current)
The negative sign in Faraday’s Law represents Lenz’s Law. This law provides the direction
of the induced current and is a direct consequence of the **Principle of Conservation of
Energy**.
Statement: The induced current flows in a direction that creates a magnetic field that
opposes the change in magnetic flux that caused it.
• If the external flux is increasing (e.g., magnet approaching the coil), the induced
magnetic field opposes the direction of the external field.
• If the external flux is decreasing (e.g., magnet moving away), the induced magnetic
field aligns with the external field to try and maintain the original flux.
The external work done to overcome this opposition is converted into electrical energy in
the circuit, thus conserving energy.
1
, 2 Motional Electromotive Force (EMF)
When a conducting rod of length l moves with a constant velocity v perpendicular to a
uniform magnetic field B, a potential difference is induced across its ends. This is called
Motional EMF.
2.1 Derivation
As the rod moves, the free charges (q) within it experience a magnetic force F~B = q(~v × B).
~
This force pushes the positive charges to one end and negative charges to the other, estab-
~ inside the conductor. Equilibrium is reached when the magnetic
lishing an electric field E
force equals the electric force (qE = qvB), so E = vB.
The induced EMF (E) is the voltage across the length l:
E = El = Blv
• Power Required: To keep the rod moving, an external mechanical force must coun-
teract the magnetic drag force (Fdrag = IlB), where I = E/R = Blv/R.
• The power input (work done by external force) Pmech = Fext v exactly equals the elec-
trical power dissipated in the resistance Pelec = I 2 R, demonstrating energy conser-
vation.
2.2 Eddy Currents
When bulk metallic conductors (not just thin wires) are subjected to changing magnetic
flux, loops of current are induced within the body of the conductor itself. These internal
current loops are called Eddy Currents.
• Characteristics: Eddy currents flow perpendicular to the direction of the magnetic
field and the conductor’s motion. They are often large because the bulk metal has
very low resistance.
• Drawbacks: They dissipate energy as heat (Joule heating), leading to energy loss in
devices like transformers and motors.
• Minimization: Eddy currents are minimized by constructing cores of transformers
and motors using thin, insulated sheets (laminations) stacked parallel to the mag-
netic field. This increases the resistance of the paths the eddy currents must take.
• Applications: They are used beneficially in magnetic braking systems (e.g., in trains
or roller coasters) and in induction furnaces for melting metals.
2.3 Flux Linkage (Ψ)
The total magnetic flux coupled by a coil of N turns is called the Flux Linkage (Ψ):
Ψ = N ΦB
Using this notation, Faraday’s Law is simplified to E = − dΨ
dt .
2
1 Fundamentals and Magnetic Flux
1.1 Definition of Electromagnetic Induction (EMI)
Electromagnetic Induction is the process by which a changing magnetic field through a
conductor or a coil induces an electric current (and thus an Electromotive Force, or EMF)
in that conductor. This phenomenon, discovered by Michael Faraday in 1831, forms the
basis for nearly all modern electrical power generation.
1.2 Magnetic Flux (ΦB )
Magnetic flux is a measure of the total number of magnetic field lines passing through a
given area. A change in this quantity is the necessary condition for EMI.
The magnetic flux ΦB through an area A in a uniform magnetic field B ~ is defined as:
~ ·A
ΦB = B ~ = BA cos θ
~ and the area vector (A).
where θ is the angle between the magnetic field vector (B) ~
• Unit: The SI unit of magnetic flux is the weber (Wb), where 1 Wb = 1 Tesla · meter2
(1 T · m2 ).
• Change in Flux: Magnetic flux can change in three ways: (1) Changing the magni-
tude of B,~ (2) Changing the area A exposed to B,
~ or (3) Changing the angle θ.
1.3 Faraday’s Law of Induction
Faraday’s Law quantitatively describes the magnitude of the induced EMF (E) in a circuit.
It states that the induced EMF in a coil is directly proportional to the rate of change of
magnetic flux through the coil.
For a coil with N turns, the induced EMF is:
dΦB
E = −N
dt
• The unit of EMF is the volt (V).
• If the induced current I flows through a resistance R, the current is I = E/R.
1.4 Lenz’s Law (Direction of Induced Current)
The negative sign in Faraday’s Law represents Lenz’s Law. This law provides the direction
of the induced current and is a direct consequence of the **Principle of Conservation of
Energy**.
Statement: The induced current flows in a direction that creates a magnetic field that
opposes the change in magnetic flux that caused it.
• If the external flux is increasing (e.g., magnet approaching the coil), the induced
magnetic field opposes the direction of the external field.
• If the external flux is decreasing (e.g., magnet moving away), the induced magnetic
field aligns with the external field to try and maintain the original flux.
The external work done to overcome this opposition is converted into electrical energy in
the circuit, thus conserving energy.
1
, 2 Motional Electromotive Force (EMF)
When a conducting rod of length l moves with a constant velocity v perpendicular to a
uniform magnetic field B, a potential difference is induced across its ends. This is called
Motional EMF.
2.1 Derivation
As the rod moves, the free charges (q) within it experience a magnetic force F~B = q(~v × B).
~
This force pushes the positive charges to one end and negative charges to the other, estab-
~ inside the conductor. Equilibrium is reached when the magnetic
lishing an electric field E
force equals the electric force (qE = qvB), so E = vB.
The induced EMF (E) is the voltage across the length l:
E = El = Blv
• Power Required: To keep the rod moving, an external mechanical force must coun-
teract the magnetic drag force (Fdrag = IlB), where I = E/R = Blv/R.
• The power input (work done by external force) Pmech = Fext v exactly equals the elec-
trical power dissipated in the resistance Pelec = I 2 R, demonstrating energy conser-
vation.
2.2 Eddy Currents
When bulk metallic conductors (not just thin wires) are subjected to changing magnetic
flux, loops of current are induced within the body of the conductor itself. These internal
current loops are called Eddy Currents.
• Characteristics: Eddy currents flow perpendicular to the direction of the magnetic
field and the conductor’s motion. They are often large because the bulk metal has
very low resistance.
• Drawbacks: They dissipate energy as heat (Joule heating), leading to energy loss in
devices like transformers and motors.
• Minimization: Eddy currents are minimized by constructing cores of transformers
and motors using thin, insulated sheets (laminations) stacked parallel to the mag-
netic field. This increases the resistance of the paths the eddy currents must take.
• Applications: They are used beneficially in magnetic braking systems (e.g., in trains
or roller coasters) and in induction furnaces for melting metals.
2.3 Flux Linkage (Ψ)
The total magnetic flux coupled by a coil of N turns is called the Flux Linkage (Ψ):
Ψ = N ΦB
Using this notation, Faraday’s Law is simplified to E = − dΨ
dt .
2
