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Field of a point charge calculator

A-level Fields and space

The electric field strength at a distance from a point charge.

E = Q / (4πε₀ r²)

This free calculator is for A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.

Quantity to find

EElectric field strength to find 1120 V/m

QCharge

ε₀Permittivity of free space constant F/m

rDistance from the charge

Significant figures

Working

Write the equation
E = Q / (4πε₀ r²)
Constants used
ε₀ = 8.85 × 10⁻¹² F/m
Substitute the values
E = (5 × 10⁻⁹) ÷ (4π × (8.85 × 10⁻¹²) × 0.2²)
Calculate
E = 1123.98 V/m
Give the answer to 3 significant figures
E = 1120 V/m

Worked example

Find E, the electric field strength. Given: charge Q = 5.00 × 10⁻⁹ C; distance from the charge r = 0.200 m; permittivity of free space ε0 = 8.85 × 10⁻¹² F/m.

Write the equation
E = Q / (4πε₀ r²)
Constants used
ε₀ = 8.85 × 10⁻¹² F/m
Substitute the values
E = (5 × 10⁻⁹) ÷ (4π × (8.85 × 10⁻¹²) × 0.2²)
Calculate
E = 1123.98 V/m
Give the answer to 3 significant figures
E = 1120 V/m

Symbols and units

Symbol	Quantity	SI unit
E	Electric field strength	V/m
Q	Charge	C
ε₀	Permittivity of free space (constant)	F/m
r	Distance from the charge	m

Field of a point charge: rearranged

To find electric field strength: E = Q / (4πε₀ r²)
To find charge: Q = 4πE ε₀ r²
To find distance from the charge: r = √(Q / (4πE ε₀))

Exam tip

The field falls with the square of the distance.

Common questions

What is the formula for field of a point charge?

The equation is E = Q / (4πε0 r²), where E is the electric field strength (V/m); Q is the charge (C); r is the distance from the charge (m); ε0 is the permittivity of free space (F/m).

What units should I use for field of a point charge?

In SI units: electric field strength in V/m, charge in C, permittivity of free space in F/m, distance from the charge in m. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange E = Q / (4πε0 r²)?

Rearranging gives these forms: to find electric field strength: E = Q / (4πε0 r²). to find charge: Q = 4πE ε0 r². to find distance from the charge: r = √(Q / (4πE ε0)).

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More fields and space equations: Coulomb’s law, Uniform electric field, Electric field strength, Newton’s law of gravitation, Gravitational field strength, Gravitational potential, Orbital period, Escape velocity. See the full list on the a-level physics equation calculator page.