Lorenz's Power

Содержание и основные понятия

The magnetic force of Lorenz is perpendicular to the speed and therefore does not work. It changes direction, but not the speed module.
GEF · 11 grade
PIF · Baseline
Interactive model
Lorenz's power
cyclotron
Mass spectrometer
vintage trajectory
01
The physical picture
What happens and what boundaries the model has.
Main message
The magnetic force of Lorenz is perpendicular to the speed and therefore does not work. It changes direction, but not the speed module.
At v perpendicular to B, the trajectory is a circle.
The longitudinal component of speed creates a screw line.
The charge mark changes the direction of the warp.
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.
F
=
∣
q
∣
v
B
sin
⁡
α
F = |q|vB\sin\alpha
F
=
∣
q
∣
v
B
sin
α
The magnetic force of Lorenz
R
=
m
v
∣
q
∣
B
R = \frac{mv}{|q|B}
R
=
∣
q
∣
B
m
v
​
radii of trajectory at v V
Review of the situation
In a homogeneous field, particles with a high pulse are moving along the circle of a larger radius.
04
Links and application
In the real world
In a homogeneous field, particles with a high pulse are moving along the circle of a larger radius.
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 "Lorenza Force" through a model, not just a formula.
Outcome 2
Clear and correctly use terms: Lorenz's power, cyclotron, mass spectrometer.
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.
Lorenz's power
Power for charged particle in electrical and magnetic fields.
cyclotron
Charged particle accelerator using magnetic field and variable electric field.
Mass spectrometer
A device separating the ions from the mass to the charge and measuring their composition.
vintage trajectory
The trajectory of the charged particle from the longitudinal and transverse to the magnetic field of the speed components.
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.
F
=
∣
q
∣
v
B
sin
⁡
α
F = |q|vB\sin\alpha
F
=
∣
q
∣
v
B
sin
α
empirical law
The power of the Lorenz.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
F
⃗
=
q
v
⃗
×
B
⃗
\vec F=q\,\vec v\times\vec B
F
=
q
v
×
B
Experiments with moving charges give Lorenz the magnetic force a vector work.
∣
v
⃗
×
B
⃗
∣
=
v
B
sin
⁡
α
|\vec v\times\vec B|=vB\sin\alpha
∣
v
×
B
∣
=
v
B
sin
α
The vector work module is defined by a cross-sectional speed component to the field.
F
=
∣
q
∣
v
B
sin
⁡
α
F=|q|vB\sin\alpha
F
=
∣
q
∣
v
B
sin
α
The charge module gives the force module, and the q sign changes its direction to the opposite.
Conditions:
The precision charge q moves at v in magnetic field B; α is the angle between v and B; the electrical component of the force is not taken into account here.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
R
=
m
v
∣
q
∣
B
R = \frac{mv}{|q|B}
R
=
∣
q
∣
B
m
v
​
model effect
The trajectory radius.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
F
L
=
∣
q
∣
v
B
F_L=|q|vB
F
L
​
=
∣
q
∣
v
B
When moving perpendicular to the field, Lorenz's power has the maximum unit and is always perpendicular to speed.
F
ц
=
m
v
2
R
F_{\text{ц}}=\frac{mv^2}{R}
F
c/
​
=
R
m
v
2
​
Such a force plays a centrifugal role and does not change the speed module.
∣
q
∣
v
B
=
m
v
2
R
⇒
R
=
m
v
∣
q
∣
B
|q|vB=\frac{mv^2}{R}\quad\Rightarrow\quad R=\frac{mv}{|q|B}
∣
q
∣
v
B
=
R
m
v
2
​
⇒
R
=
∣
q
∣
B
m
v
​
The equalization of forces gives the radius of the circle.
Conditions:
The non-relativist particle moves perpendicularly to uniform B; other forces are missing, v 0.
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 transfer the formula to any situation just because it's a coincidence of letters. The key condition of this topic is that if v is perpendicular to B, the trajectory is a circle.
How to Check the Mind
The longitudinal component of speed creates a screw line. Then check the units, the direction of the vectors and the behaviour of the result at zero or very large parameter.
Σ
Conclusion on the topic
Lorenz's Power
The magnetic force of Lorenz is perpendicular to the speed and therefore does not work. It changes direction, but not the speed module.
At v perpendicular to B, the trajectory is a circle.
The longitudinal component of speed creates a screw line.
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.