Electromagnetic induction

Содержание и основные понятия

The change in the magnetic field that cuts through the circuit creates an induction current. The current direction is such that its field is opposed to the cause of the change.
GEF · Grade 9
PIF · Baseline
Interactive model
Magnetic flux
Induction current
Lenz rule.
Generator
01
The physical picture
What happens and what boundaries the model has.
Main message
The change in the magnetic field that cuts through the circuit creates an induction current. The current direction is such that its field is opposed to the cause of the change.
It's about changing the magnetic flow, not just having a strong field.
The rapid movement of the magnet or more turns increases the effect.
The phenomenon is at the core of generators, transformers and induction sensors.
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.
Φ
=
B
S
cos
⁡
α
\Phi=BS\cos\alpha
Φ
=
BS
cos
α
Magnetic flux
∣
ε
i
∣
∼
∣
Δ
Φ
∣
Δ
t
|\varepsilon_i|\sim\frac{|\Delta\Phi|}{\Delta t}
∣
ε
i
​
∣
∼
Δ
t
∣ΔΦ∣
​
EDS inductions
Review of the situation
If you move the magnet into the coil and then move it, the galvanometer deviates in opposite directions.
04
Links and application
In the real world
If you move the magnet into the coil and then move it, the galvanometer deviates in opposite directions.
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 "Electromagnetic Induction" through the model, not just the formula.
Outcome 2
Distinguish and correctly use terms: magnetic flow, induction current, 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.
Magnetic flux
A scalar measure of the magnetic field that penetrates the selected surface.
Induction current
Electrical current in a closed loop caused by the change in magnetic flow through it.
Lenz rule.
The inductive current is directed so that the field it creates is counterproductive to the change in magnetic flow.
Generator
A device that converts mechanical or other energy into electrical energy.
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.
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.
S
⊥
=
S
cos
⁡
α
S_{\perp}=S\cos\alpha
S
⊥
​
=
S
cos
α
The field effective area is the projection of the site on a plane perpendicular to the magnetic induction vector.
Φ
≡
B
S
⊥
\Phi\equiv B S_{\perp}
Φ
≡
B
S
⊥
​
The magnetic flow through a flat contour into a homogeneous field is defined as B multiplied by the directional transverse area.
Φ
=
B
S
cos
⁡
α
\Phi=BS\cos\alpha
Φ
=
BS
cos
α
The setting of the area projection takes into account the orientation of the normal to the contour relative to the field.
Conditions:
Flat surface area S in a homogeneous magnetic field; α is the angle between B and the normal to the surface.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
∣
ε
i
∣
∼
∣
Δ
Φ
∣
Δ
t
|\varepsilon_i|\sim\frac{|\Delta\Phi|}{\Delta t}
∣
ε
i
​
∣
∼
Δ
t
∣ΔΦ∣
​
empirical law
Eds induction.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
Δ
Φ
≠
0
⇒
ε
i
≠
0
\Delta\Phi\ne0\Rightarrow\varepsilon_i\ne0
ΔΦ

=
0
⇒
ε
i
​

=
0
Faraday's experience reveals the presence of EDS in the contour of a change in magnetic flow.
∣
ε
i
∣
∝
∣
Δ
Φ
∣
,
∣
ε
i
∣
∝
1
Δ
t
|\varepsilon_i|\propto|\Delta\Phi|,\quad |\varepsilon_i|\propto\frac{1}{\Delta t}
∣
ε
i
​
∣
∝
∣ΔΦ∣
,
∣
ε
i
​
∣
∝
Δ
t
1
​
Measurements show that large changes in flow and less time for change result in larger EDS.
∣
ε
i
∣
∼
∣
Δ
Φ
∣
Δ
t
|\varepsilon_i|\sim\frac{|\Delta\Phi|}{\Delta t}
∣
ε
i
​
∣
∼
Δ
t
∣ΔΦ∣
​
This proportionality is experimentally established; the direction of current separates the Lenz rule, and the exact law for one turn contains a minus.
Conditions:
The variable magnetic flow through the closed circuit; the recording gives the relationship of the medium EDS module, and the N turns have a multiplier N.
Monitoring:
The proportionality shall be verified; the dimension of full equality shall restore the factor omitted.
!
Model boundaries and typical errors
Error: Forget model condition
You can't change the formula to any situation just because it's a coincidence of letters. The key condition of this topic is that change in magnetic flow is important, not just the presence of a strong field.
How to Check the Mind
The rapid movement of the magnet or more turns increases the effect. Then check the units, vector direction, and behavior of the result at zero or very large parameter.
Σ
Conclusion on the topic
Electromagnetic induction
The change in the magnetic field that cuts through the circuit creates an induction current. The current direction is such that its field is opposed to the cause of the change.
It's about changing the magnetic flow, not just having a strong field.
The rapid movement of the magnet or more turns increases the effect.
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.