Law of electromagnetic induction

Содержание и основные понятия

The EDS in the outline is the rate of change of the magnetic flow with the sign expressing the Lenz rule. The flow can be changed by field, area or shape of the outline.
GEF · 11 grade
PIF · Baseline
Interactive model
EDS inductions
flux adhesion
Lenz rule.
swirl currents
01
The physical picture
What happens and what boundaries the model has.
Main message
The EDS in the outline is the rate of change of the magnetic flow with the sign expressing the Lenz rule. The flow can be changed by field, area or shape of the outline.
A constant stream doesn't create an EDS, even if the field itself is large.
The number of turns multiplys the sum of the chaining.
Lenz's rule is a manifestation of energy conservation.
How to reason
First, name the system and the interaction, then select the values, and only then write down the law. The formula works within the model's assumptions.
02
Laws and values
Symbols should be read as a relationship of values, not as a recipe for substitution.
E
i
=
−
N
Δ
Φ
Δ
t
\mathcal{E}_i=-N\frac{\Delta\Phi}{\Delta t}
E
i
​
=
−
N
Δ
t
ΔΦ
​
Faraday Law
Φ
=
B
S
cos
⁡
α
\Phi = BS\cos\alpha
Φ
=
BS
cos
α
Magnetic flux
Review of the situation
Rotation in a permanent field changes flow periodically and creates an EDS variable.
04
Links and application
In the real world
Rotation in a permanent field changes flow periodically and creates an EDS variable.
Model verification
Compare the prediction with observation, evaluate the units, the order of magnitude and the influence of the factors not taken into account. Disparity does not always mean an error of law: often idealization is no longer sufficient.
C
What needs to be understood
Outcome 1
Explain the physical meaning of the topic "The Law of Electromagnetic Induction" through a model, not just a formula.
Outcome 2
Distinguish and correctly use terms: EDS inductions, flow chaining, Lenz rule.
Outcome 3
Indicate the conditions for the applicability of the law, verify units and limit cases.
T
Terms of the topic
The definition should indicate the physical meaning, not a substitute for a domestic synonym.
EDS inductions
Operation of a swirl electric field to carry a single charge along the contour.
flux adhesion
The sum of magnetic flows through all turns of the contour; for the same turns, is N.
Lenz rule.
The inductive current is directed so that the field it creates is counterproductive to the change in magnetic flow.
swirl currents
Locked induction currents that occur in the volume of the conductor when the magnetic flow changes.
F
Origin and conclusion of the formulas
The fundamental law cannot be "proven" by algebras: for each record, it is stated whether it is a definition, an experimental law, or a model effect.
E
i
=
−
N
Δ
Φ
Δ
t
\mathcal{E}_i=-N\frac{\Delta\Phi}{\Delta t}
E
i
​
=
−
N
Δ
t
ΔΦ
​
empirical law
The Faraday Law.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
∣
E
i
∣
∝
N
|\mathcal{E}_i|\propto N
∣
E
i
​
∣
∝
N
Measurements show that EDS coils are proportional to the number of equally slapping turns.
∣
E
i
∣
∝
∣
Δ
Φ
Δ
t
∣
|\mathcal{E}_i|\propto \left|\frac{\Delta\Phi}{\Delta t}\right|
∣
E
i
​
∣
∝
​
Δ
t
ΔΦ
​
​
The faster the magnetic flow changes through the turns, the bigger the EDS module.
E
i
=
−
N
Δ
Φ
Δ
t
\mathcal{E}_i=-N\frac{\Delta\Phi}{\Delta t}
E
i
​
=
−
N
Δ
t
ΔΦ
​
The minus sign expresses Lenz's rule: the induced current is opposed to the flow change.
Conditions:
The average EDS over the interval Δt in the N turns coil; the flow through the turns is the same. For the instantaneous value, the derivative of -N dø/dt shall be used.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
Φ
=
B
S
cos
⁡
α
\Phi = BS\cos\alpha
Φ
=
BS
cos
α
definition
Magnetic flux.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
Φ
:
=
∫
S
B
⃗
⋅
d
S
⃗
\Phi:=\int_S\vec B\cdot d\vec S
Φ
:=
∫
S
​
B
⋅
d
S
Magnetic flux is defined as the flow of vector B through the directional surface.
B
⃗
=
c
o
n
s
t
⇒
Φ
=
B
S
cos
⁡
α
\vec B=\mathrm{const}\quad\Rightarrow\quad\Phi=BS\cos\alpha
B
=
const
⇒
Φ
=
BS
cos
α
For a flat surface in a homogeneous field, the integral becomes a scalar product B and an area vector.
Conditions:
The flat surface of area S in a homogeneous field, α is the angle between B and normal to the surface.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
!
Model boundaries and typical errors
Error: Forget model condition
The key condition of this topic is that the constant flow does not create an EDS, even if the field itself is large.
How to Check the Mind
The number of turns multiplys the total chaining. Then check the units, vector direction and result behaviour at zero or very large parameter.
Σ
Conclusion on the topic
Law of electromagnetic induction
The EDS in the outline is the rate of change of the magnetic flow with the sign expressing the Lenz rule. The flow can be changed by field, area or shape of the outline.
A constant stream doesn't create an EDS, even if the field itself is large.
The number of turns multiplys the sum of the chaining.
Any numerical result shall be accompanied by a unit, a sign and an explanation of its physical meaning.
The content is consistent with the FRP on Physics of the OS/OSS 2025 and the subject matter of the current lines of the PNP: I. M. Peryškin and co-authors (7–9), G. J. Mäkishev and coauthors (10–11), and with the lines "Engineers of the Future" and V. A. Kasyanov. The original texts are not reproduced, the text of the textbooks is not reproduced.