Theme D — Fields

D.2.9 Electric Potential Gradient — IB Physics HL Revision Notes & Topical Questions

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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 = V_f − V_i

Point charge

ΔV = kQ(1/r_f − 1/r_i), 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

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

Forgetting the minus sign and giving the wrong direction.

Using E = V/d for non-uniform fields.

Reading V from the graph instead of the slope when finding E.

Taking the field to be zero where V is zero.

Mixing the units — V m⁻¹ and N C⁻¹ are the same.

Last updated: 15 October 2026

Part 1 of 7Work done on a charge

Part 2 of 7Potential gradient

Part 3 of 7Uniform field

Part 4 of 7Point charge: the V–r graph

Part 5 of 7Point charge: the E–r graph

Part 6 of 7Checks and links

Part 7 of 7More from the specification

Key terms

Avoid these mistakes

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