Amper's Power

Содержание и основные понятия

The magnetic field operates on the conductor with current because it operates on moving charges inside it. The force is maximized when the conductors and fields are perpendicular.
GEF · 11 grade
PIF · Baseline
Interactive model
Magnetic induction
Amper's power
Current frame
magnetic torque
01
The physical picture
What happens and what boundaries the model has.
Main message
The magnetic field operates on the conductor with current because it operates on moving charges inside it. The force is maximized when the conductors and fields are perpendicular.
The direction is determined by the rule of the left hand for positive current.
The parallel currents of the same direction are drawn.
The current frame in the field is experiencing a torque.
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
=
B
I
l
sin
⁡
α
F = B I l \sin\alpha
F
=
B
I
l
sin
α
Amper's power
M
=
B
I
S
sin
⁡
α
M = B I S \sin\alpha
M
=
B
I
S
sin
α
time frame
Review of the situation
A guide parallel to the field lines does not test Amper's powers, although the current and field are non-zero.
04
Links and application
In the real world
A guide parallel to the field lines does not test Amper's powers, although the current and field are non-zero.
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 Force of Amper" through the model, not just the formula.
Outcome 2
Distinguish and correctly use terms: magnetic induction, ampere force, current frame.
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 induction
Vector force characteristic of the magnetic field measured in tesla.
Amper's power
Power from magnetic field to current conductor.
Current frame
Locked circuit with current with magnetic torque.
magnetic torque
A vector characteristic of the magnetic field source, determining its orientation and its interaction with the external field.
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
=
B
I
l
sin
⁡
α
F = B I l \sin\alpha
F
=
B
I
l
sin
α
empirical law
Amper power.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
F
∝
I
l
F \propto I l
F
∝
I
l
Experience shows that the force on the direct section of the conductor is proportional to the current and length of the area in the field.
F
∝
B
F \propto B
F
∝
B
Magnetic induction B shall be introduced so that the perpendicular conductor fulfils F = Bil.
l
⊥
=
l
sin
⁡
α
l_{\perp}=l\sin\alpha
l
⊥
​
=
l
sin
α
A cross-sectional dimension of length is active to the field, so the sine α multiplier is formed.
Conditions:
A direct guide of length l with constant current I in a homogeneous field B; α is the angle between the direction of current and B.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
M
=
B
I
S
sin
⁡
α
M = B I S \sin\alpha
M
=
B
I
S
sin
α
model effect
It's a time frame.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
F
=
B
I
l
F=BIl
F
=
B
I
l
On the two opposite sides, the field operates by the forces of Amper, which form a pair of forces.
M
=
F
a
=
B
I
l
a
=
B
I
S
M=Fa=BIl\,a=BI S
M
=
F
a
=
B
I
l
a
=
B
I
S
For a rectangular frame, the shoulder of the pair is a, and the product of la is equal to the area of S.
M
=
B
I
S
sin
⁡
α
M=BI S\sin\alpha
M
=
B
I
S
sin
α
The slope shall be taken into account as an area perpendicular to the field; α is the angle between the normal to the frame and B.
Conditions:
One spin of flat rigid frame with current I in a homogeneous field; the size of the frame is small compared to the size B.
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 formula cannot be moved to any situation simply because of the coincidence of the letters. The key condition of this topic is that the direction is defined by the rule of the left hand for positive current.
How to Check the Mind
The parallel currents of the same direction are drawn. Then check the units, vector direction and result behaviour at zero or very large parameter.
Σ
Conclusion on the topic
Amper's Power
The magnetic field operates on the conductor with current because it operates on moving charges inside it. The force is maximized when the conductors and fields are perpendicular.
The direction is determined by the rule of the left hand for positive current.
The parallel currents of the same direction are drawn.
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.