Theme D — Fields

D.2.5 Electric Field Strength — IB Physics HL Revision Notes & Topical Questions

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D.2.5 Electric Field Strength — IB PHYSICS SL notes: Define electric field strength and calculate it for point charges, combined charges and the uniform field between parallel plates.Electric field — a region of space in which a charged object experiences an electric forceThe fie…

Electric field strength (E)
What the symbols mean
Inverse-square field
Charged sphere
Superposition
Right-angled geometry

Section 1 of 10The electric field

The electric field

Electric field

Electric field a region of space in which a charged object experiences an electric force
The field concept describes the effect of a charge on its surroundings whether or not a second charge is present.

Electric field strength (E)

Electric field strength (E) the force per unit charge experienced by a small positive test charge at that point
E = F / q
What the symbols mean: E = electric field strength (N C⁻¹) · F = force on the charge (N) · Q or q = charge (C)
E is in N C⁻¹, which equals V m⁻¹.

Vector

E is directed away from a positive charge and towards a negative charge
A positive charge feels a force qE in the direction of the field.
A negative charge feels a force opposite to E, so F = qE with sign included.

Section 2 of 10Field of a point charge

Equation

E = kQ / r² = Q / (4πε₀r²)
It follows from combining E = F/q with Coulomb's law.
Q is the source charge, not the test charge.

Inverse-square field

Inverse-square field doubling the distance reduces E to a quarter

Graphs

E against r is a decaying curve and E against 1/r² is a straight line with gradient kQ

Charged sphere

Charged sphere outside it the field is identical to that of a point charge of the same total charge at the centre
Inside a charged conducting sphere the field strength is zero.

Section 3 of 10Combining fields

Superposition

Superposition to find the field at a point due to several charges, add the individual fields as vectors

Same line

Same line add the magnitudes if the fields point the same way and subtract them if they point opposite ways

Right-angled geometry

Right-angled geometry use Pythagoras for the resultant of perpendicular fields

Direction

Direction treat the point as a positive test charge, so fields point away from positive charges and towards negative charges

Section 4 of 10Uniform field between parallel plates

1Uniform field

Uniform field a field with the same magnitude and direction at every point

2Parallel plates

Parallel plates two large oppositely charged plates give a uniform field between them, except near the edges

3Direction

Direction the field points from the positive plate to the negative plate

4Equation

E = V / d
What the symbols mean: E = uniform electric field strength (V m⁻¹) · V = p.d. between the plates (V) · d = plate separation (m)
V is the potential difference and d the plate separation.
A greater voltage gives a stronger field and a greater separation gives a weaker one.

5Units

1 V m⁻¹ = 1 N C⁻¹

6Validity

E = V/d applies only to the uniform field and not to a point charge, whose field is radial

7Force on a charge

F = qE = qV/d, a constant force

8Earthed plate

Earthed plate if one plate is earthed it is at 0 V

Section 5 of 10Charged particles in uniform fields

Charged particles in uniform fields

Acceleration

Acceleration it is constant, a = qE/m, so the constant-acceleration equations apply

From rest

From rest the particle moves in a straight line along the field
Its speed after distance d is v = √(2qEd/m).
This agrees with the energy result ½mv² = qV.

Entering across the field

Entering across the field motion along the plates is at constant speed and motion across them is uniformly accelerated
The path is a parabola, y = (qE/2mv²)x², like a projectile in a gravitational field.

Applications

Applications oscilloscopes and inkjet printers deflect charged particles with a voltage across plates

Weight

Weight for small particles such as electrons, the electric force is so large that weight is neglected

Section 6 of 10Comparison with the gravitational field

Analogy

E is the electrical analogue of g, defined as force per unit charge and falling as 1/r² for point sources

Differences

Electric field lines begin on positive charges and end on negative charges, so the force can attract or repel.
Gravity only attracts.
Acceleration in an electric field is qE/m, not E.

Millikan

Millikan in his experiment the force qE balanced the weight of an oil drop

Section 7 of 10Magnetic analogue

Magnetic fields are covered in D.2.11 and the motion of charges in magnetic fields in D.3

Section 8 of 10More from the specification

1Electric field mapping

Electric field mapping evaluating electric force per unit positive test charge provides a rigorous means to define electric field intensity.

2Electric Field Strength and Coulomb's Law

Electric field strength is defined as force per unit positive test charge (E = F/q = Q / (4πε₀r²)), depending on the permittivity of the surrounding material.

3Charge Distribution on Conducting Surfaces

Electrostatic charge on a conductor resides entirely on its outer surface,
where surface charge density and localized electric field strength are greatest at points of sharpest curvature.

4Electrostatic Contact and Charge Sharing

When identical conducting spheres are brought into physical contact, charge redistributes equally across their surfaces due to repulsive Coulomb forces.

5Magnetic Dipole Analogy

Just as magnetic field lines run from north to south poles, electric field lines emanate outward from positive charges and terminate on negative charges.

6Permittivity

A property of a medium affecting the electric force within it.

7Current

Flow of electrons in a circuit.

8Density

Mass per unit volume.

9Relative permittivity

Ratio of the permittivity of a material to that of free space.

10W = mg

What the symbols mean: W = weight (N) · m = mass (kg) · g = gravitational field strength (9.81 N kg⁻¹ on Earth)

Section 9 of 10Key terms

Term	Meaning
Electric field strength E	Force per unit positive charge, N C⁻¹.
Test charge	A small positive charge used to probe a field.
Uniform field	Constant field, as between parallel plates.
E = kQ/r²	Field of a point charge.
E = V/d	Field between parallel plates.

Section 10 of 10Exam technique

Treating E as a scalar — it has direction.

Forgetting that a negative charge feels a force opposite to E.

Using E = V/d for a point charge — it applies only to a uniform field.

Using the test charge in the point-charge formula kQ/r^{2} — Q is the source.

Mixing up N C^{−1} and V m^{−1} — they are equivalent.

Last updated: 18 October 2026