10.1Electric fields and capacitance (A Level)

Electric Fields

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Lesson summary

10.1 Electric Fields — AS PHYSICS 9702 notes: Use electric field strength, Coulomb's law, electric potential and the motion of charges in uniform fields.Electric field — a region of space in which a charge experiences a forceField strength — E = F/q, the force per unit positive c…

What the symbols mean
Force on a charge
Spherical conductor
Force and acceleration
Radial field
Several charges

Section 1 of 10Electric field and field strength

Electric field

Electric field a region of space in which a charge experiences a force

Field strength

E = F/q, the force per unit positive charge
What the symbols mean: E = electric field strength (N C⁻¹) · F = force on the charge (N) · Q or q = charge (C)

Direction

Direction the direction of the force on a positive charge, away from positive and towards negative

Force on a charge

F = qE

Section 2 of 10Field lines

Meaning

Meaning lines show the direction of force on a positive charge

Uniform field

Uniform field parallel, equally spaced lines

Spherical conductor

Spherical conductor for a point outside it, the charge may be treated as a point charge at its centre

Section 3 of 10Uniform field between parallel plates

Field strength

E = ΔV/Δd between parallel plates

Force and acceleration

Force and acceleration a charge q experiences a constant force qE and acceleration qE/m

Path

Path a charge entering at right angles to the field follows a parabola

Section 4 of 10Coulomb's law and radial fields

Coulomb's law

Coulomb's law the force between two point charges is proportional to the product of the charges and inversely proportional to the square of their separation

Equation

F = Q₁Q₂/(4πε₀r²)
ε₀ = 8.85 × 10⁻¹² F m⁻¹ and 1/(4πε₀) = 8.99 × 10⁹ m F⁻¹

Radial field

E = Q/(4πε₀r²), an inverse-square law

Several charges

Several charges fields add as vectors

Section 5 of 10Electric potential

1Definition

Definition the work done per unit positive charge in bringing a small test charge from infinity to the point

2Point charge

V = Q/(4πε₀r), positive around a positive charge, negative around a negative charge and zero at infinity

3Scalar

Scalar potentials add algebraically

4Potential energy of two charges

E_p = Qq/(4πε₀r)

Section 6 of 10Potential gradient

Relation

E = −ΔV/Δr, so the field strength is minus the gradient of a V–r graph

Work

Work moving a charge q through a potential difference ΔV needs work qΔV

Section 7 of 10Charged particle in a uniform field

Charged particle in a uniform field

The electron enters midway between the plates with horizontal speed v

Horizontally there is no force

Horizontally there is no force the time in the field is t = L/v

Vertically the force is eE

Vertically the force is eE the acceleration is a = eE/m

Vertical deflection

Vertical deflection y = ½at²

Path

Path a parabola inside the field and a straight line outside it

Section 8 of 10More from the specification

Section 9 of 10Key terms

Term	Meaning
Electric field strength	force per unit positive charge, E = F/q
Electric potential	work done per unit positive charge bringing a test charge from infinity
Coulomb's law	force between two point charges proportional to Q₁Q₂/r²
Permittivity of free space	ε₀ = 8.85 × 10⁻¹² F m⁻¹
Potential gradient	the rate of change of potential with distance, equal to −E
Uniform field	a field with the same strength and direction everywhere

Section 10 of 10Exam technique

Using the plate formula for a point charge — E = V/d applies only to uniform fields between parallel plates.

Adding potentials as vectors — potential is a scalar, add algebraically.

Forgetting the direction for a negative charge — the force is opposite to the field.

Taking E as plus the gradient of V — E equals minus the potential gradient.