Switch electromagnetic field

Содержание и основные понятия

The changing magnetic field creates a vortex electric field, and the changing electric field is magnetic, and together they form a single electromagnetic field.
GEF · Grade 9
PIF · Baseline
Interactive model
Electromagnetic field
Swirl field
variable current
Field energy
01
The physical picture
What happens and what boundaries the model has.
Main message
The changing magnetic field creates a vortex electric field, and the changing electric field is magnetic, and together they form a single electromagnetic field.
The vortex electric field is independent of the charges and has closed power lines.
Switched fields may exist far from the input charges and currents.
The power is stored and transported by the electrical and magnetic components of the field.
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
⃗
⟷
B
⃗
\vec E\longleftrightarrow\vec B
E
⟷
B
The relationship of variable fields
c
=
1
ε
0
μ
0
c=\frac{1}{\sqrt{\varepsilon_0\mu_0}}
c
=
ε
0
​
μ
0
​
​
1
​
Wave speed in vacuum
Review of the situation
In the antenna, variable current creates changing fields that separate from the source and spread through space.
04
Links and application
In the real world
In the antenna, variable current creates changing fields that separate from the source and spread through space.
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 "Transformed electromagnetic field" through the model, not just through the formula.
Outcome 2
Clear and correctly use terms: electromagnetic field, vortex field, AC current.
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.
Electromagnetic field
A single field, the electrical and magnetic components of which are connected.
Swirl field
A field with closed lines of power, the circulation of which on a closed circuit may be non-zero.
variable current
Electrical current, the size and usually the direction of which changes periodically over time.
Field energy
Energy contained in the physical field and capable of being transferred to the substance or other fields.
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
⃗
⟷
B
⃗
\vec E\longleftrightarrow\vec B
E
⟷
B
Postulate or Model
The relationship of variable fields.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
∂
B
⃗
∂
t
≠
0
⇒
rot
⁡
E
⃗
≠
0
\frac{\partial\vec B}{\partial t}\ne0\Rightarrow\operatorname{rot}\vec E\ne0
∂
t
∂
B
​

=
0
⇒
rot
E

=
0
Electromagnetic induction shows that a changing magnetic field creates a vortex electric field.
rot
⁡
B
⃗
=
μ
0
J
⃗
+
μ
0
ε
0
∂
E
⃗
∂
t
\operatorname{rot}\vec B=\mu_0\vec J+\mu_0\varepsilon_0\frac{\partial\vec E}{\partial t}
rot
B
=
μ
0
​
J
+
μ
0
​
ε
0
​
∂
t
∂
E
​
The magnetic field is related to both conductivity current J and electrical field change. In a vacuum at J = 0, the non-zero \E/\t creates a non-negative vortex B.
E
⃗
⟷
B
⃗
\vec E\longleftrightarrow\vec B
E
⟷
B
A two-way arrow is a qualitative record of the mutual creation of variable fields rather than an independent numerical equality.
Conditions:
The time-changing electromagnetic fields; the symbol \ transmits a quality connection and does not replace the equations of the Marshall. The direct relationship of the change E to the vortex B is formulated for a vacuum without conductivity current.
Monitoring:
The symbol shows a causal link, not an equality; it checks the direction of change and the physical mechanism.
c
=
1
ε
0
μ
0
c=\frac{1}{\sqrt{\varepsilon_0\mu_0}}
c
=
ε
0
​
μ
0
​
​
1
​
model effect
Wave speed in the vacuum.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
∇
2
E
⃗
=
μ
0
ε
0
∂
2
E
⃗
∂
t
2
\nabla^2\vec E=\mu_0\varepsilon_0\frac{\partial^2\vec E}{\partial t^2}
∇
2
E
=
μ
0
​
ε
0
​
∂
t
2
∂
2
E
​
In the vacuum of the Maxwell equation for the variable fields, you combine into a wave equation.
∇
2
E
⃗
=
1
c
2
∂
2
E
⃗
∂
t
2
\nabla^2\vec E=\frac{1}{c^2}\frac{\partial^2\vec E}{\partial t^2}
∇
2
E
=
c
2
1
​
∂
t
2
∂
2
E
​
The standard wave equation contains a factor 1/c2 before the second derivative in time.
1
c
2
=
ε
0
μ
0
⇒
c
=
1
ε
0
μ
0
\frac{1}{c^2}=\varepsilon_0\mu_0\Rightarrow c=\frac{1}{\sqrt{\varepsilon_0\mu_0}}
c
2
1
​
=
ε
0
​
μ
0
​
⇒
c
=
ε
0
​
μ
0
​
​
1
​
Comparison of coefficients connects electromagnetic wave speed to electrical and magnetic constants.
Conditions:
The electromagnetic wave spread in the vacuum; \_0 and μ_0 are vacuum constants, environment and dispersion are not available.
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
You can't move the formula to any situation just because it's a coincidence of letters. The key condition of this topic is that the vortex electric field isn't just connected to the charges and has closed power lines.
How to Check the Mind
The variable fields may exist far from the input charges and currents. Then check the units, vector direction and result behaviour at zero or very large parameter.
Σ
Conclusion on the topic
Switch electromagnetic field
The changing magnetic field creates a vortex electric field, and the changing electric field is magnetic, and together they form a single electromagnetic field.
The vortex electric field is independent of the charges and has closed power lines.
Switched fields may exist far from the input charges and currents.
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.