Capacity and Field Work

Содержание и основные понятия

The potential is equal to the potential energy of the single positive charge. The voltage is the difference of the potential that determines the field's operation when the charge is transferred.
GEF · 10 grade
PIF · Baseline
Interactive model
capacity
voltage
Equivalent surface
Field operation
01
The physical picture
What happens and what boundaries the model has.
Main message
The potential is equal to the potential energy of the single positive charge. The voltage is the difference of the potential that determines the field's operation when the charge is transferred.
The electrostatic field is potentially zero.
The equivalent surfaces are perpendicular to the voltage lines.
The positive charge is spontaneously moving towards less potential.
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
=
W
п
q
\varphi=\frac{W_{\mathrm{п}}}{q}
φ
=
q
W
c/
​
​
capacity
A
1
→
2
=
q
(
φ
1
−
φ
2
)
A_{1\to2}=q(\varphi_1-\varphi_2)
A
1
→
2
​
=
q
(
φ
1
​
−
φ
2
​
)
Field operation
E
=
U
d
E=\frac{U}{d}
E
=
d
U
​
uniform field
Review of the situation
The electron moves against the direction E because its charge is negative, and it can increase kinetic energy.
04
Links and application
In the real world
The electron moves against the direction E because its charge is negative, and it can increase kinetic energy.
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 capacity and work of the field" through the model, not just through the formula.
Outcome 2
Identify and correctly use terms: potential, stress, equivalent surface.
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.
capacity
Field scalar energy characteristic: potential energy of a single positive charge.
voltage
The difference between the capabilities of the two points is equal to the field's work in carrying the single charge.
Equivalent surface
A surface whose electrical potential is the same at all points.
Field operation
Power supplied by the electric field of charge when it moved.
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
=
W
п
q
\varphi=\frac{W_{\mathrm{п}}}{q}
φ
=
q
W
c/
​
​
definition
Potential.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
W
п
∝
q
W_{\mathrm{п}}\propto q
W
c/
​
∝
q
In a given electrostatic field, the potential energy of the test charge is proportional to its size.
φ
≡
W
п
q
\varphi\equiv\frac{W_{\mathrm{п}}}{q}
φ
≡
q
W
c/
​
​
The ratio independent of the test charge is defined as the potential of the field at the point.
W
п
=
q
φ
W_{\mathrm{п}}=q\varphi
W
c/
​
=
qφ
The potential charge energy at the point is determined by the selected potential and zero.
Conditions:
The electrostatic potential field; q × 0 and small enough not to change the field; the zero level of capacity shall be specified.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
A
1
→
2
=
q
(
φ
1
−
φ
2
)
A_{1\to2}=q(\varphi_1-\varphi_2)
A
1
→
2
​
=
q
(
φ
1
​
−
φ
2
​
)
model effect
Fieldwork.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
A
1
→
2
=
−
Δ
W
п
=
W
п
,
1
−
W
п
,
2
A_{1\to2}=-\Delta W_{\mathrm{п}}=W_{\mathrm{п},1}-W_{\mathrm{п},2}
A
1
→
2
​
=
−
Δ
W
c/
​
=
W
c/
,
1
​
−
W
c/
,
2
​
The operation of the electrostatic force is equal to the loss of potential energy.
W
п
,
1
=
q
φ
1
,
W
п
,
2
=
q
φ
2
W_{\mathrm{п},1}=q\varphi_1,\quad W_{\mathrm{п},2}=q\varphi_2
W
c/
,
1
​
=
q
φ
1
​
,
W
c/
,
2
​
=
q
φ
2
​
The potential energy of the charge is related to the potential of each point.
A
1
→
2
=
q
(
φ
1
−
φ
2
)
A_{1\to2}=q(\varphi_1-\varphi_2)
A
1
→
2
​
=
q
(
φ
1
​
−
φ
2
​
)
The quadrupling of the difference gives the field a function.
Conditions:
Fixed electrostatic field and constant charge q; field operation is independent of trajectory between points 1 and 2.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
E
=
U
d
E=\frac{U}{d}
E
=
d
U
​
model effect
A homogeneous field.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
A
=
q
E
d
A=qEd
A
=
qE
d
In a homogeneous field, the force of qE is constant, and when moving along the field to d, its work is qEd.
A
=
q
U
A=qU
A
=
q
U
The work at charge transfer through the range of U potentials is qU.
q
E
d
=
q
U
⇒
E
=
U
d
qEd=qU\quad\Rightarrow\quad E=\frac{U}{d}
qE
d
=
q
U
⇒
E
=
d
U
​
The matching of the two expressions of work and the abbreviation of q gives the formula.
Conditions:
A homogeneous electrostatic field, the movement d is directed along the power line; for a flat capacitor, the lateral effects are ignored.
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 transferred to any situation simply because of the overlap of letters. The key condition of this topic is that the electrostatic field is potentially: the work on the closed loop is zero.
How to Check the Mind
The equivalent surfaces are perpendicular to the voltage lines. Then check the units, vector direction and result behaviour at zero or very large parameter.
Σ
Conclusion on the topic
Capacity and Field Work
The potential is equal to the potential energy of the single positive charge. The voltage is the difference of the potential that determines the field's operation when the charge is transferred.
The electrostatic field is potentially zero.
The equivalent surfaces are perpendicular to the voltage lines.
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.