OCR Specification focus:
‘Define potential at a point as work done per unit positive charge from infinity; potential is zero at infinity.’
Electric potential is a concept describing how electric fields do work on charges, enabling energy analysis and clarifying interactions between charged objects across varying distances.
Electric Potential and Its Physical Meaning
Electric potential is a fundamental idea used to quantify how an electric field influences charged particles. It provides a way to describe the energy landscape around charged objects, allowing us to understand how and why charges move. The OCR specification emphasises that potential is defined relative to infinity, where potential is taken to be zero. This convention underpins all potential and electric potential energy calculations in electrostatics and ensures consistency when analysing fields created by isolated point or spherical charges.
When a charge moves in an electric field, work is done either by the field or against it. Electric potential gives a direct measure of the work done per unit positive charge in bringing a small test charge from infinity to a point in the field. This approach avoids the complications of dealing with the test charge’s own influence on the field, ensuring the concept applies universally to point charges, spherical charges, and extended fields.
Formal Definition of Electric Potential
The concept of electric potential enables us to shift from thinking in terms of forces, which depend on the charge experiencing them, to thinking in terms of energy per unit charge, which depends only on position.
Electric potential: The work done per unit positive charge in bringing a small test charge from infinity to a point in an electric field, taking the potential at infinity as zero.
This definition links electric potential directly to the idea of energy changes in electric fields, making it a scalar quantity that varies smoothly through space. Because it is a scalar, electric potential also avoids the directional complications associated with electric field vectors.
A point in space has a single definite potential due to a given arrangement of charges. This value may be positive, negative, or zero, depending on whether work must be done against or by the field in moving a positive charge to that point. This distinction helps students interpret diagrams and apply potential-difference relationships correctly.
Relationship Between Electric Potential and Work
Understanding electric potential requires a clear grasp of how electric fields perform work. Moving a positive test charge against the field requires external work, increasing its potential; moving it with the field allows the field to do work, reducing its potential. These ideas underpin electric potential energy calculations introduced later in the syllabus.
Normal physical situations involve differences in potential rather than absolute potential values. However, the OCR specification requires awareness that the defined reference point is infinity, where potential is zero. This convention is especially important when dealing with isolated point charges. As you move further away from the charge, the field weakens and the potential approaches zero, matching the specification’s requirement.
Because potential is defined in terms of work per unit charge, the movement of any positive charge in an electric field is associated with a change in potential energy that is proportional to the potential difference between points. This helps explain physical phenomena such as electron acceleration in electric fields, though detailed motion analysis belongs elsewhere in the syllabus.
Equation for Electric Potential
For a point charge, the electric potential at a distance from the charge can be expressed mathematically. This equation is essential when quantifying how potential varies with radial distance.
EQUATION
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Electric potential of a point charge (V) = V = (1/(4πɛ₀)) · (Q/r)
V = electric potential at the point (volt, V)
Q = source charge creating the field (coulomb, C)
r = distance from the charge to the point (metre, m)
ε₀ = permittivity of free space (farad metre⁻¹, F m⁻¹)
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This expression shows that potential decreases with increasing distance from the charge, consistent with the requirement that potential tends to zero at infinity. It also emphasises the importance of inverse proportionality to distance, a key feature of radial electric fields.
The equation highlights several crucial properties:
Electric potential depends only on the source charge and the distance.
It is independent of the value of any test charge placed in the field.
The sign of the potential matches the sign of the source charge, supporting intuitive reasoning about attraction and repulsion.
Interpreting Electric Potential in Field Diagrams
Electric potential can be visualised using equipotential surfaces, which connect points of equal potential.
Equipotential circles around a single point charge with radial electric field lines. Moving along an equipotential requires no work, whereas moving between them changes potential. The figure highlights that equipotentials are everywhere perpendicular to electric field lines. Source.
These surfaces are always perpendicular to electric field lines, reflecting how no work is needed to move a charge along them.
Field lines and equipotential lines surrounding a positive point charge. Work is needed only to move between equipotentials, never along them. The original page includes nearby context about conductors, but this figure itself focuses only on point-charge equipotentials. Source.
Key interpretive points include:
Positive charges create regions of positive potential, while negative charges create regions of negative potential.
Near a point charge, equipotential surfaces are concentric spheres, illustrating how potential varies radially.
The potential gradient between equipotentials corresponds to electric field strength, though the syllabus treats detailed field–potential relationships elsewhere.
Practical Importance of Electric Potential
Electric potential is indispensable in analysing electrical energy transfer. It supports reasoning about:
how much work must be done to assemble charge distributions
the direction of spontaneous charge movement
the energy changes occurring when charges move in circuits or fields
These applications rely fundamentally on the OCR-defined relationship between work, charge, and the reference point at infinity.
FAQ
Electric potential refers to work done per unit positive charge and is a property of a location in an electric field. It does not depend on the value of any test charge placed there.
Electric potential energy refers to the total work associated with a specific charge at that location.
• Potential is position-dependent only.
• Potential energy depends on both position and the charge placed at that position.
A positive test charge provides a consistent convention for describing the direction of electric fields and the sign of potential changes.
Using a negative test charge would reverse the direction of force and potential differences, complicating the interpretation of field behaviour. The positive-charge convention ensures that potential increases when moving against the field and decreases when moving with it.
Electric potential is continuous everywhere except at the location of point charges themselves.
At the position of a point charge, the potential becomes undefined because the distance to the charge approaches zero.
• Away from charges, potential varies smoothly and predictably.
• Abrupt changes only arise from modelling assumptions such as idealised point charges or infinitely thin charge distributions.
Yes. Electric potential is a scalar quantity and can result from many different charge arrangements producing identical net work per unit charge.
This means:
• Two different configurations may yield the same potential at one location but different potentials elsewhere.
• Identical potentials do not guarantee identical electric fields, because field direction and magnitude depend on vector contributions rather than scalar sums.
The electric field weakens with distance, so the change in potential per metre (the potential gradient) decreases further from the source charge.
As a result:
• Larger physical distances are required to produce the same change in potential.
• Equipotentials spread out, reflecting the diminishing influence of the charge at greater distances.
Practice Questions
Question 1 (2 marks)
Define electric potential at a point in an electric field. Explain why the potential at infinity is taken to be zero.
Mark scheme:
• Electric potential is the work done per unit positive charge in bringing a charge from infinity to a point in the field. (1)
• Infinity is taken as zero potential because the electric field is negligible at infinite separation, providing a consistent reference point. (1)
Question 2 (5 marks)
A positively charged particle is moved from infinity to a point P near an isolated positive point charge.
(a) Explain what is meant by electric potential at point P.
(b) The electric potential at point P is +4500 V. Describe, with reasoning, whether work must be done by or against the electric field to bring the particle from infinity to point P.
(c) State two features of equipotential surfaces around an isolated point charge and explain how each feature relates to the definition of electric potential.
Mark scheme:
(a)
• Electric potential at P is the work done per unit positive charge in bringing a charge from infinity to P. (1)
(b)
• Potential is positive, indicating the source charge is positive. (1)
• Work must be done against the electric field because like charges repel. (1)
(c)
Any two of the following, with explanation:
• Equipotential surfaces are perpendicular to electric field lines. (1)
– Because no work is done when moving a charge along an equipotential, matching the definition of potential involving work. (1)
• Equipotential surfaces around a point charge are concentric spheres. (1)
– Reflecting that potential depends only on distance from the charge, consistent with radial variation in work done. (1)
• No work is required to move a charge along an equipotential. (1)
– Because potential does not change along these surfaces, so work per unit charge is zero. (1)
