OCR Specification focus:
‘Define electric field strength E = F/q as force per unit positive charge.’
Electric field strength is a central idea in electrostatics, describing how strongly an electric field can push or pull a charged object. Understanding this concept allows students to interpret interactions between charges in terms of forces and explains why electric fields shape the behaviour of charged particles across many physical systems.
Electric field strength measures how strongly an electric field acts on a charge. It provides a quantitative link between electric forces and the sources producing the surrounding field region.
Electric Field Strength: The Core Concept
Electric fields are regions around charges where forces are exerted on other charges. When a charge is placed in such a region, it experiences a force due to the presence of another charge or system of charges. The idea of electric field strength captures how intense this influence is at any given position in space.
Electric Field Strength: The force per unit positive charge acting at a point in an electric field.
This definition emphasises that electric field strength is not about the test charge itself but about the nature of the field at that location. By always defining it with respect to a positive test charge, physicists maintain a consistent convention for the direction of electric fields: they point in the direction a positive charge would accelerate.
The electric field strength at a point is defined as the force per unit positive charge placed at that point.
Electric field around a uniformly negatively charged sphere showing the force F on a positive test charge and the electric field vector E at that point. The diagram also includes electric field lines pointing towards the negative sphere, illustrating how field line direction matches the direction of the force on a positive test charge. The detailed pattern of field lines and the explicit separation between force and field vectors are slightly beyond the syllabus, but they reinforce the definition of electric field strength as force per unit positive charge. Source.
Electric field strength is therefore a vector quantity, possessing both magnitude and direction, and can vary from point to point depending on the distribution of surrounding charges.
Mathematical Expression for Field Strength
The formal expression for electric field strength follows directly from Newton’s second law principles and the interaction between charges. When a small positive test charge is placed in an electric field and experiences a force, the field strength at that point can be found using the equation below.
EQUATION
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Electric Field Strength (E) = F / q
E = Electric field strength, measured in newtons per coulomb (N C⁻¹)
F = Force experienced by the test charge, measured in newtons (N)
q = Magnitude of the test charge, measured in coulombs (C)
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This relationship is foundational: it allows electric fields to be quantified experimentally by applying a known charge and measuring the force on it. While later subsubtopics introduce field strength due to a point charge, the present focus is solely the definition, ensuring students first grasp the meaning of the quantity before applying formulae derived from Coulomb’s law.
Because the formula uses the force on a test charge, the test charge must be small enough that it does not disturb or alter the field being measured. This ensures that the calculated field strength reflects the original electric field, not one influenced by the test charge itself.
Direction and Representation of Electric Field Strength
The direction of E at a point is defined as the direction in which a positive charge would move. This convention ensures consistency across diagrams, equations, and descriptions. In practical terms:
If two like charges are brought near each other, the field lines and therefore E point away from each charge.
If opposite charges are used, field lines and E point from the positive charge towards the negative charge.
A neutral point, where field vectors cancel, has E = 0, meaning a charge placed there experiences no net force.
Field lines always point in the direction that a positive test charge would move: away from positive charges and towards negative charges.
Electric field line diagrams for a single positive charge (left) and a single negative charge (right). Arrows show the direction a positive test charge would move, away from the positive charge and towards the negative charge. The way the lines cluster closely near each charge visually represents regions of stronger electric field, slightly beyond syllabus requirements but helpful for conceptual clarity. Source.
Although field line representations are treated in a different subsubtopic, it is still important here to recognise that the density of field lines corresponds to the magnitude of electric field strength. A region with tightly packed lines represents a strong field, while sparse lines show a weak field.
Factors Affecting Electric Field Strength at a Point
Even at this introductory stage, it is helpful to emphasise the variables that determine electric field strength in general scenarios, though the precise mathematical forms are addressed elsewhere. Key influences include:
Distance from the source charge or distribution: electric fields become weaker with increasing separation.
Magnitude of the source charge: a larger charge produces a stronger field.
Geometry of the charge distribution: whether a point charge, sphere, plate, or more complex shape, the arrangement affects how the field spreads out in space.
Presence of other charges nearby: superposition of fields from multiple charges alters the resultant field strength.
Students should remember that electric field strength always describes the field at a point, meaning it can form complex patterns in space when multiple charges interact.
Physical Significance and Usefulness
Electric field strength links the abstract idea of a field to the measurable quantity of force. This makes it particularly useful in understanding a variety of physical systems, such as:
The behaviour of electrons in conductors and insulators
The operation of particle accelerators and cathode-ray tubes
Forces acting on ions in electric fields, important in chemistry and biology
The interactions governing capacitors and electric potential differences
The influence of electric fields within atoms and molecules
By defining the electric field through its effect on a positive test charge, physicists obtain a universal description applicable across microscopic and macroscopic scales. This allows electric fields to be treated in a similar conceptual way to gravitational fields, though significant differences arise in later studies.
In summary, the definition of electric field strength provides the essential stepping stone for all further work in electrostatics, ensuring students understand how forces emerge from charge distributions and how these forces can be both predicted and analysed quantitatively.
FAQ
Using a positive test charge establishes a universal convention for field direction. If a negative test charge were used instead, the indicated direction of the field would reverse, creating inconsistency across diagrams, definitions, and formulae.
This convention ensures that electric field lines, force vectors, and standard equations all align with the same directional framework, making communication and interpretation far clearer in physics.
The test charge must be small enough that it does not noticeably alter the original electric field. There is no fixed numerical limit, because this depends on the strength of the source charge and the sensitivity of the system.
In practice, the test charge should satisfy:
• It does not cause significant redistribution of charge on nearby conductors.
• It does not create an additional electric field large enough to distort the one being measured.
Electric field strength can change rapidly over small distances if the field originates from a point charge or a sharply curved surface. The field weakens quickly as distance increases.
However, in regions far from charges or between large parallel plates, the variation over small distances may be negligible.
Whether E varies significantly depends on:
• The geometry of the source charges
• The distance from those charges
• Whether multiple fields are overlapping
Yes. Electric field strength can be zero at locations where the electric fields from multiple charges cancel exactly.
This occurs at points where:
• The fields from different charges have equal magnitude
• The directions of the field vectors are directly opposite
• Superposition results in a net field of zero
These points are often called equilibrium points, although they may not be stable.
Electric field strength describes the force per unit charge, so any charged particle experiences a force proportional to both its charge and the field strength at its location.
However, unlike a test charge, a real charged particle may:
• Alter the electric field in the region
• Interact dynamically with other charges
• Cause redistribution of charge on nearby conductors
The definition of electric field strength remains valid, but the particle’s own influence on the system must sometimes be considered in deeper analyses.
Practice Questions
Question 1 (2 marks)
A positive test charge experiences a force of 3.0 × 10⁻⁴ N when placed at a particular point in an electric field. The test charge has a magnitude of 2.0 × 10⁻⁶ C.
Calculate the electric field strength at this point and state its direction.
Question 1 (2 marks)
• Correct calculation of electric field strength:
E = 3.0 × 10⁻⁴ / 2.0 × 10⁻⁶ = 150 N C⁻¹ (1 mark)
• Correct statement of direction:
Electric field acts in the direction a positive charge would move (away from positive charges or towards negative charges). (1 mark)
Question 2 (5 marks)
Explain what is meant by electric field strength. Your answer should refer to both magnitude and direction. Describe how the concept of a positive test charge is used in defining electric field strength, and explain why the test charge must be sufficiently small. Finally, outline how field line patterns can be used to indicate variations in electric field strength in a region.
Question 2 (5 marks)
• States that electric field strength is the force per unit positive charge. (1 mark)
• Identifies that electric field strength has both magnitude and direction, making it a vector quantity. (1 mark)
• Explains that a positive test charge is used to define the direction of the field. (1 mark)
• States that the test charge must be small enough not to disturb the electric field. (1 mark)
• Describes how field line density indicates the relative strength of the electric field (closer lines mean stronger field). (1 mark)
