Theme D — Fields
D.2.9 Electric Potential Gradient — IB Physics HL Revision Notes & Topical Questions
5 min read 9 parts Lesson 24 of 39 1 quiz
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Lesson summary
D.2.9 Electric Potential Gradient — IB PHYSICS HL notes: Use E = −ΔV/Δr and the V–r and E–r graphs to relate electric field strength and potential.Equation — W = qΔVSymbols — q is the charge moving in the field and ΔV the potential difference in VPotential difference — ΔV = Vf − …
- Point charge
- Distinguish
- Definition
- Minus sign
- Steeper line
- Positive charge
Part 1 of 7Work done on a charge
Equation
- W = qΔV
Symbols
- Symbols q is the charge moving in the field and ΔV the potential difference in V
Potential difference
- ΔV = Vf − Vi
Point charge
- ΔV = kQ(1/rf − 1/ri), where Q produces the potential
Distinguish
- Distinguish q is the charge moved and Q the charge producing the potential
Part 2 of 7Potential gradient
Definition
- Definition the rate of change of electric potential with displacement in the direction of the field
Equation
- E = −ΔV/Δr
Unit
- Unit volts per metre, equal to newtons per coulomb
Minus sign
- Minus sign the field points in the direction in which the potential falls, from high to low potential
Force
- F = qE = −q ΔV/Δr
Part 3 of 7Uniform field
Potential
- Potential it changes linearly from the positive plate to the negative plate
V–d graph
- V–d graph a straight line with constant gradient −V/d
Field
- E = V/d is uniform
Steeper line
- Steeper line a stronger field
Midway
- Midway the potential is half the plate voltage
Part 4 of 7Point charge: the V–r graph
Equation
- V = kQ/r
Positive charge
- V is positive, falling with distance as 1/r
Negative charge
- V is negative, rising towards zero as −1/r
Gradient
- Gradient dV/dr = −kQ/r2, so E = kQ/r2
Steepness
- Steepness the field is large where the curve is steep near the charge and small where it flattens
Estimating E
- E ≈ −(V2 − V1)/(r2 − r1) between two close points
Part 5 of 7Point charge: the E–r graph
Equation
- E = kQ/r2, an inverse square law
Signs
- E is positive for a positive charge and negative for a negative charge
Area
- Area the area under an E–r graph between two points is the potential difference
Uniform field
- Uniform field the area is a rectangle, ΔV = Ed
Compared with V–r
- Compared with V–r the E–r curve is steeper than the V–r curve
Part 6 of 7Checks and links
Field zero
- Field zero where the V–r graph has zero gradient, even if V is not zero
Direction check
- Direction check the field must point towards decreasing potential
Magnitude check
- Magnitude check the gradient and field decrease with distance
Gravity analogy
- Gravity analogy g = −ΔV/Δr
Part 7 of 7More from the specification
More from the specification
Electric fields versus magnetic fields
- Electric fields versus magnetic fields electrostatic fields exert forces on static charges,
- while Earth's magnetic fields deflect circulating charge carriers.
Electric Potential Gradient and Field Strength
- The electric field strength E at any location is equal to the negative gradient of electric potential (E = -dV/dr),
- meaning electric field lines point directly down the potential gradient.
Equipotential Surfaces and Work Done
- Equipotential surfaces connect points of identical electric potential;
- moving a charge along an equipotential surface requires zero work (W = q ΔV = 0),
- and electric field lines always cross equipotentials at right angles.
Potential Distribution Between Parallel Plates
- Between oppositely charged parallel conducting plates separated by distance d with potential difference V, equipotential lines are parallel planes spaced uniformly across the gap.
Electric Potential of a Charged Conducting Sphere
- For an isolated conducting sphere of radius R carrying charge Q in a medium of permittivity ε, the electric potential is uniform across the entire surface and interior (V = Q / 4πεR) and falls inversely with distance r outside.
Electric Potential Gradient and Field Strength
- The electric field strength E at any location is equal to the negative gradient of electric potential (E = -dV/dr),
- meaning electric field lines point directly down the potential gradient.
Equipotential Surfaces and Work Done
- Equipotential surfaces connect points of identical electric potential;
- moving a charge along an equipotential surface requires zero work (W = q ΔV = 0),
- and electric field lines always cross equipotentials at right angles.
Potential Distribution Between Parallel Plates
- Between oppositely charged parallel conducting plates separated by distance d with potential difference V, equipotential lines are parallel planes spaced uniformly across the gap.
Electric Potential of a Charged Conducting Sphere
- For an isolated conducting sphere of radius R carrying charge Q in a medium of permittivity ε, the electric potential is uniform across the entire surface and interior (V = Q / 4πεR) and falls inversely with distance r outside.
Equipotential
- A surface of constant potential
Parallel
- Components on separate branches, each with the full e.m.f.
Permittivity
- A property of a medium affecting the electric force within it.
Current
- Flow of electrons in a circuit.
Density
- Mass per unit volume.
Field lines
- Lines showing the direction and strength of a magnetic field.
Magnetic field
- Area around a magnet where its effects can be detected.
Potential energy
- Energy stored by the configuration of a system.
Key terms
| Term | Meaning |
|---|---|
| Potential gradient | The rate of change of electric potential with displacement in the direction of the field. |
| E = −ΔV/Δr | The electric field strength equals the negative potential gradient. |
| Uniform field | A field with the same strength and direction at every point, E = V/d between parallel plates. |
| Work done on a charge | W = qΔV, the charge times the potential difference. |
Avoid these mistakes
1
Forgetting the minus sign and giving the wrong direction.
2
Using E = V/d for non-uniform fields.
3
Reading V from the graph instead of the slope when finding E.
4
Taking the field to be zero where V is zero.
5
Mixing the units — V m−1 and N C−1 are the same.
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