Electric potential (A-level only) — AQA A-Level Physics

Electric potential is a fundamental concept in A-level Physics that describes the electric potential energy per unit charge at a point in an electric field. It allows us to analyse fields without considering the test charge, and it is crucial for understanding how charges move and how energy is stored in electric fields. This topic extends your knowledge of electric fields and gravitational fields, highlighting the similarities between the two.

In the AQA A-level specification, electric potential is a key part of the 'Fields and their consequences' module. You will learn to calculate potential due to point charges, understand equipotential surfaces, and relate potential to field strength. This concept is essential for later topics such as capacitance and the motion of charged particles in electric fields, and it frequently appears in exam questions involving calculations and explanations.

• →Electric potential at a point is the work done per unit positive charge in bringing a small positive test charge from infinity to that point. It is a scalar quantity measured in volts (V), where 1 V = 1 J C^-1.
• →The electric potential due to a point charge Q at a distance r is given by V = kQ/r, where k = 1/(4*pi*epsilon_0) = 8.99x10^9 N m^2 C^-2. The potential is positive for positive charges and negative for negative charges, and it approaches zero at infinity.
• →The total electric potential at a point due to several point charges is the algebraic sum of the potentials due to each charge individually. This is because potential is a scalar quantity.
• →The electric field strength E is related to the potential gradient by E = -dV/dr. The negative sign indicates that the electric field points in the direction of decreasing potential.
• →Equipotential surfaces are surfaces on which the electric potential is constant. No work is done when a charge moves along an equipotential surface, and the electric field lines are always perpendicular to these surfaces.

• Defines absolute electric potential as work done per unit positive charge in bringing a small positive test charge from infinity to the point: V = W/Q.
• States that the zero of electric potential is at infinity, where the electric field is zero.
• Uses V = kQ/r for the potential at distance r from a point charge Q, recognising that V is a scalar and can be positive or negative.
• Defines electric potential difference as the work done per unit positive charge in moving between two points: ΔV = W/Q.
• Calculates potential difference from the potentials at two points, ΔV = V₂ − V₁, and uses it to find energy transferred W = QΔV.
• Uses correct units: volts (V) or joules per coulomb (J C⁻¹) for potential and potential difference.
• State that electric potential V is work done per unit positive charge: V = W/Q, with the test charge brought from infinity.
• Use W = QΔV to calculate energy transferred when charge Q moves through a potential difference ΔV, ensuring consistent signs for energy gain or loss.
• Define an equipotential surface as a surface where the electric potential is constant, so ΔV = 0 between any two points on it.
• Explain that equipotential surfaces are always perpendicular to electric field lines, and sketch them for a uniform field (parallel planes) and a radial field (concentric spheres).
• Relate the direction of motion to work done: if a positive charge moves to a higher potential, work is done on the charge; if it moves to a lower potential, the field does work.
• State that on an equipotential surface, the potential difference between any two points is zero (ΔV = 0).
• Apply W = QΔV to show that if ΔV = 0, then W = 0, regardless of the magnitude of Q.
• Explain that the electric force is perpendicular to the equipotential surface, so the force has no component along the displacement.
• Relate this to the definition of work done: W = Fs cosθ, where θ = 90°, so cos90° = 0 and W = 0.
• Give a practical example, such as a charge moving on a spherical equipotential around a point charge, or a charge moving along the surface of a charged conductor.

• 💡When calculating potential due to several point charges, sum the scalar values algebraically, taking account of positive and negative charges.
• 💡Use ΔV = W/Q to link potential difference to energy transfer, and rearrange carefully to find W, Q or ΔV as required.
• 💡Check the sign of your answer: potential near a positive charge is positive, and near a negative charge is negative, relative to infinity.
• 💡When calculating work done, write the equation W = QΔV, substitute values with units, and state the direction of energy transfer (work done on or by the field).
• 💡For equipotential sketches, always draw field lines first, then add equipotentials perpendicular to them, labelling values of potential if given.
• 💡If a question asks about moving a charge along an equipotential, immediately state that ΔV = 0, so W = 0, and explain that the electric force is perpendicular to the displacement.
• 💡When asked why no work is done, explicitly state that ΔV = 0 and that the electric force is perpendicular to the displacement.
• 💡Use the equation W = QΔV to justify the zero work done, and mention that Q is not zero but ΔV is zero.
• 💡If a diagram is given, identify the equipotential surface and show that the path lies along it, then explain the perpendicularity of force and motion.
• 💡Always define electric potential precisely: 'work done per unit positive charge in bringing a small positive test charge from infinity to that point'. Missing 'per unit positive charge' or 'from infinity' loses marks.
• 💡When calculating potential due to multiple charges, show each calculation separately and then sum them algebraically. This makes your method clear and helps you avoid sign errors.
• 💡Remember that electric field strength is the negative gradient of potential: E = -dV/dr. In graphs of V against r, the gradient gives -E, and you may be asked to interpret such graphs.

• Treating electric potential as a vector and adding potentials with direction; correction: potential is a scalar, so add or subtract algebraic values including signs.
• Forgetting that the zero of potential is at infinity and using a finite reference point; correction: always state that V = 0 at infinity when defining absolute potential.
• Confusing potential with potential energy; correction: potential is energy per unit charge, while potential energy is QV for a charge Q at potential V.
• Confusing electric potential V with electric potential energy: V is per unit charge, while potential energy is QV. Correction: always divide or multiply by Q as appropriate.
• Using W = QΔV with ΔV as a magnitude and ignoring the sign of the charge or the potential change, leading to incorrect energy direction. Correction: include signs or state clearly whether energy is gained or lost.
• Drawing equipotential surfaces that cross or are not perpendicular to field lines. Correction: equipotentials must be perpendicular to field lines everywhere and can never intersect.
• Assuming that because a force acts on the charge, work must be done. Correction: work depends on the component of force along the displacement; perpendicular forces do no work.
• Thinking that moving along an equipotential changes the potential energy of the charge. Correction: potential energy depends on potential, which is constant, so it does not change.
• Confusing equipotential surfaces with electric field lines. Correction: equipotentials are perpendicular to field lines and represent constant potential, while field lines show the direction of force on a positive charge.
• Students often think electric potential is a vector and try to add potentials using vector addition. In fact, electric potential is a scalar, so you simply add the potentials algebraically, taking into account their signs.
• Many students confuse electric potential (V) with electric potential energy (U). Potential is energy per unit charge (V = U/q), while potential energy is the energy a specific charge possesses at a point (U = qV).
• Students frequently forget that the electric potential at infinity is defined as zero. This leads to errors when calculating potential differences or work done in moving charges from infinity.

1. 1Start by revising the definition of electric potential and the formula V = kQ/r. Practice calculating potential for single point charges, ensuring you convert units correctly.
2. 2Move on to multiple charges: learn to calculate the total potential at a point by summing individual potentials algebraically. Work through examples with both positive and negative charges.
3. 3Study the relationship between electric field and potential: understand that E = -dV/dr and practice interpreting graphs of V against r, including finding gradients.
4. 4Learn about equipotential surfaces and their properties, including how they relate to field lines and work done. Sketch equipotential lines for simple charge configurations.
5. 5Complete past paper questions on electric potential, focusing on calculation and explanation questions. Review mark schemes to understand what examiners expect.

• 📋Calculation of electric potential at a point due to one or more point charges. Advice: always write the formula, substitute values with units, and keep track of signs. For multiple charges, calculate each potential separately before summing.
• 📋Explanation questions on the definition of electric potential and why it is a scalar. Advice: use precise wording: 'work done per unit positive charge in bringing a small positive test charge from infinity to that point'. Emphasise that potential is scalar and add algebraically.
• 📋Graph interpretation: given a graph of electric potential V against distance r, determine the electric field strength at a point by finding the negative gradient. Advice: draw a tangent, calculate gradient, and remember the negative sign indicates direction.
• 📋Comparison of electric and gravitational potential: discuss similarities and differences. Advice: focus on the inverse square law, scalar nature, and the fact that gravitational potential is always negative while electric potential can be positive or negative.