Coulomb’s law — OCR A-Level Physics
Test yourself on Coulomb’s law with OCR A-Level practice questions.
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Coulomb’s law explained
Coulomb’s law gives the magnitude of the electrostatic force between two point charges in a vacuum or air.
Read the full explanation
The force is proportional to the product of the charges Q and q, and inversely proportional to the square of their separation r. The constant 1/(4πε₀) is approximately 8.99 × 10⁹ N m² C⁻², where ε₀ is the permittivity of free space. The force acts along the line joining the charges: like charges repel, unlike charges attract. For example, two charges of +2.0 × 10⁻⁶ C and +3.0 × 10⁻⁶ C separated by 0.10 m experience a repulsive force of about 5.4 N. The law applies strictly to point charges; for extended charged objects it is exact only outside a spherically symmetric charge distribution.
(b) electric field strength E = Q / (4πε₀r²) for a point charge
The electric field strength E at a distance r from a point charge Q is the force per unit positive charge placed at that point. For a point charge in a vacuum or air, E = Q / (4πε₀r²). The field is radial: it points away from a positive charge and towards a negative charge. The magnitude follows an inverse-square law, so doubling r reduces E to one quarter. For example, a point charge of +4.0 × 10⁻⁹ C produces a field of about 4.0 × 10² N C⁻¹ at 0.30 m. The equation applies to point charges and outside spherically symmetric charge distributions; inside a uniform spherical shell the field is zero.
(c) similarities and differences between the gravitational field of a point mass and the electric field of a point charge
Both gravitational and electric fields of point objects obey inverse-square laws: g = GM/r² and E = Q/(4πε₀r²). Both are radial and extend to infinity. However, gravitational fields are always attractive because mass is always positive, while electric fields can be attractive or repulsive because charge can be positive or negative. The gravitational constant G is universal and very small, making gravity the weakest fundamental force, whereas the electrostatic constant 1/(4πε₀) is much larger, so electric forces between charged particles are far stronger. Also, gravitational field strength is force per unit mass, while electric field strength is force per unit positive charge. Both fields can be represented by field lines, and both follow the principle of superposition.
(d) the concept of electric fields as being one of a number of forms of field giving rise to a force.
A field is a region of space in which a suitable object experiences a force. Electric fields are one of several forms of field, alongside gravitational, magnetic and nuclear fields. An electric field exists around any charged object and exerts a force on any other charge placed in it. The force can be attractive or repulsive, depending on the signs of the charges. The concept of a field allows action at a distance to be described without invoking direct contact. For example, the electric field of a point charge can be represented by radial field lines, and the force on a test charge is given by F = qE. Fields are vector quantities and obey superposition.
Your focus
- Recall and apply Coulomb’s law in the form F = Qq / (4πε₀r²).
- Determine the magnitude and direction of the force between two point charges.
- Explain the limitations of Coulomb’s law for extended charge distributions.
Show all 12 objectives
- Define electric field strength and state its units.
- Apply E = Q / (4πε₀r²) to calculate the field of a point charge.
- Describe the direction of the electric field around positive and negative point charges.
- Compare the mathematical form and physical meaning of gravitational and electric fields of point objects.
- Explain the origin of the attractive nature of gravity and the attractive or repulsive nature of electric forces.
- Evaluate the relative strengths of gravitational and electric forces in a given physical situation.
- Define a field and give examples of different types of field.
- Explain how an electric field exerts a force on a charge.
- Represent electric fields using field lines and describe their properties.
Coulomb’s law exam tips
Marking Points
- States that the force is proportional to the product of the two charges, Qq.
- States that the force is inversely proportional to the square of the separation, r².
- Uses the constant 1/(4πε₀) with value approximately 8.99 × 10⁹ N m² C⁻².
- Recognises that the force acts along the line joining the charges and is repulsive for like charges and attractive for unlike charges.
- Applies the law only to point charges or outside spherically symmetric distributions.
- Defines electric field strength as force per unit positive charge.
- Uses the equation E = Q / (4πε₀r²) for a point charge.
- Recognises that E is a vector directed radially away from positive charge and towards negative charge.
- Applies the inverse-square dependence on distance r.
- States that the equation is valid for point charges or outside spherically symmetric distributions.
- States that both gravitational and electric fields of point masses/charges follow an inverse-square law with distance.
- States that both fields are radial and act along the line joining the point object and the test point.
- States that gravitational fields are always attractive, whereas electric fields can be attractive or repulsive.
- States that gravitational field strength is force per unit mass, while electric field strength is force per unit positive charge.
- Compares the relative strengths: the electrostatic constant 1/(4πε₀) is much larger than G, so electric forces between elementary particles are much stronger than gravitational forces.
- Recognises that both fields obey the principle of superposition and can be represented by field lines.
- Defines a field as a region where a force acts on a suitable object.
- Identifies electric fields as one of several forms of field, such as gravitational, magnetic and nuclear.
- States that electric fields arise from electric charge and exert forces on other charges.
- Recognises that electric forces can be attractive or repulsive.
- Uses the concept of a field to explain action at a distance.
Examiner Tips
- 💡Write the equation as F = Qq / (4πε₀r²) and substitute values only after converting to SI units.
- 💡Check the sign of the force to decide attraction or repulsion, and state the direction relative to the line joining the charges.
- 💡For multiple-choice questions, eliminate options that show F proportional to r or F proportional to 1/r rather than 1/r².
- 💡State the direction of E relative to the sign of the source charge before calculating its magnitude.
- 💡Convert all distances to metres and charges to coulombs before substituting into the equation.
- 💡In multiple-choice questions, check that the units of the options are N C⁻¹ and that the distance dependence is inverse-square.
- 💡Structure your answer into similarities and differences, using clear comparative language such as ‘both’, ‘whereas’ and ‘however’.
- 💡Include the equations for both field strengths and refer to the meaning of each symbol.
- 💡Use a concrete example, such as the hydrogen atom, to illustrate the dominance of electric force over gravitational force between a proton and an electron.
- 💡Use the definition ‘force per unit positive charge’ when describing electric field strength.
- 💡Link the concept of a field to the force equation F = qE when explaining how a charge experiences a force.
- 💡In multiple-choice questions, distinguish between scalar fields (e.g. temperature) and vector fields (e.g. electric, gravitational).
Common Mistakes
- Using r instead of r² in the denominator; the inverse-square dependence must be applied, so doubling r quarters the force.
- Forgetting to convert distances to metres or charges to coulombs before substitution; all SI units must be used consistently.
- Treating the force as a scalar without direction; Coulomb’s law gives magnitude, and the direction must be determined from the signs of the charges.
- Applying the point-charge formula inside a charged sphere; the field and force inside a uniform spherical shell are zero, and inside a uniform solid sphere the enclosed charge changes with r.
- Confusing electric field strength with electric potential; field strength is a vector with units N C⁻¹, while potential is a scalar with units V.
- Using the test charge q in the numerator instead of the source charge Q; the field of a point charge depends only on the source charge and the distance.
- Forgetting to square the distance; E is proportional to 1/r², not 1/r.
- Claiming that gravitational fields can be repulsive; they are always attractive because mass is always positive.
- Stating that electric field strength is force per unit charge without specifying positive charge; the direction is defined for a positive test charge.
- Assuming that the inverse-square law applies inside extended bodies; it applies outside spherically symmetric distributions.
- Confusing the constants G and 1/(4πε₀) or their relative magnitudes; G is about 6.67 × 10⁻¹¹ N m² kg⁻², while 1/(4πε₀) is about 8.99 × 10⁹ N m² C⁻².
- Thinking that a field requires a medium to exist; electric fields can exist in a vacuum.
- Confusing the field with the force; the field is a property of space, while force depends on the object placed in the field.
- Assuming that electric field lines can cross; field lines never cross because the field direction is unique at each point.
- Believing that electric fields are always uniform; the field of a point charge is radial and non-uniform.