Electric fields

• Gravity with two signs: the same inverse-square shapes as chapter 13, but because charge can be + or −, forces can repel and potentials can be positive.
• Force per unit positive charge; work per unit positive charge from infinity; the field points downhill in potential; and the sign of the charge decides the sign of V and EP.

• 18.1.1 I can understand — understand that an electric field is an example of a field of force and define electric field as force per unit positive charge
• 18.1.2 I can recall — recall and use F = qE for the force on a charge in an electric field
• 18.1.3 I can — represent an electric field by means of field lines
• 18.2.1 I can recall — recall and use E = ΔV / Δd to calculate the field strength of the uniform field between charged parallel plates
• 18.2.2 I can describe — describe the effect of a uniform electric field on the motion of charged particles
• 18.3.1 I can understand — understand that, for a point outside a spherical conductor, the charge on the sphere may be considered to be a point charge at its centre
• 18.3.2 I can recall — recall and use Coulomb's law F = Q₁Q₂/(4πε₀r²) for the force between two point charges in free space
• 18.4.1 I can recall — recall and use E = Q/(4πε₀r²) for the electric field strength due to a point charge in free space
• 18.5.1 I can define — define electric potential at a point as the work done per unit positive charge in bringing a small test charge from infinity to the point
• 18.5.2 I can recall — recall and use the fact that the electric field at a point is equal to the negative of potential gradient at that point
• 18.5.3 I can use — use V = Q/(4πε₀r) for the electric potential in the field due to a point charge
• 18.5.4 I can understand — understand how the concept of electric potential leads to the electric potential energy of two point charges and use E_P = Qq/(4πε₀r)

Two similarities and two differences, ready to write. Similar: both force laws are inverse-square laws between point sources; both potentials are defined as work done per unit (mass or positive charge) bringing a test object from infinity, and fall as 1/r. Different: gravity only attracts, while electric forces attract or repel; gravitational potential and potential energy are always negative, while electric ones take the sign of the charges.

• “Electric potential is negative, like gravitational potential.” Correct The sign of the charge decides the sign of V and of EP. \(V = Q/(4\pi\varepsilon_0 r)\) is positive round a positive charge and negative round a negative one; \(E_\mathrm{P} = Qq/(4\pi\varepsilon_0 r)\) is positive for like charges and negative for unlike ones. Substitute the charges with their signs and there is no separate minus sign to add.
• “Field strength is the force on a charge.” Correct It is the force per unit positive charge, E = F/q, in N C−1 (= V m−1). Drop “per unit” or “positive” and the definition is incomplete.
• “An electron moves along the field lines.” Correct Field lines show the force on a positive charge. The force on an electron is opposite to E, so it is pushed towards the positive plate.
• “Between the plates the electron slows down along the plates as it is deflected.” Correct The force eE is across the plates only, so the velocity component along them is unchanged; the path is a parabola, like a projectile's. After the plates it is a straight line.
• “Where the field is zero, the potential is zero.” Correct E is minus the potential gradient. Between two positive charges E = 0 at a point where V is large and positive; midway between + and − charges V = 0 where E is large.
• “Add the potentials as vectors; add the fields as numbers.” Correct The other way round. Potential is a scalar: add with signs. Field strength is a vector: add with directions.
• “r is the distance from the surface of the sphere.” Correct r is measured from the centre: outside a charged spherical conductor, its charge acts as a point charge there.
• “Electric field strength is the force on a charge.” Repair It is the force per unit positive charge on a small stationary test charge, E = F/q, in N C−1 = V m−1.
• “The field between the plates is strongest near the positive plate.” Repair It is uniform, E = V/d, everywhere between the plates away from the edges. The potential is highest near the positive plate; the field depends on its gradient, which is constant.
• “An electron moves along the field lines.” Repair Field lines show the force on a positive charge. The force on an electron is opposite to the field.
• “An electron between the plates follows a circular arc.” Repair The force eE is constant in size and direction, so the path is a parabola, as for a projectile. A circle needs a force that stays perpendicular to the velocity and changes direction with it: that is a magnetic force (chapter 20).
• “Between the plates the electron's speed along the plates decreases as it is deflected.” Repair There is no force along the plates, so that component is unchanged. Only the component across the plates changes, so the speed increases overall.
• “r is measured from the surface of the sphere.” Repair From the centre: outside a spherical conductor its charge acts as a point charge at its centre. Between two spheres, r is centre to centre.
• “Doubling the separation halves the force.” Repair Coulomb's law is inverse-square: doubling r quarters the force.
• “The larger charge exerts the larger force.” Repair The forces on the two charges are equal and opposite (Newton's third law): the same product Q1Q2 appears in both.
• “Electric potential, like gravitational potential, is always negative.” Repair It has the sign of the charge creating it: positive near a positive charge (the agent must push the test charge in), negative near a negative one (the agent must hold it back).
• “V = Q/(4πε0r2) and E = Q/(4πε0r).” Repair The other way round: V ∝ 1/r, E ∝ 1/r2. Check the units: Q/(ε0r) is in V, Q/(ε0r2) in V m−1.
• “Where the field is zero, the potential is zero.” Repair E is minus the potential gradient. At the neutral point of worked example 4, E = 0 but V = +270 V.
• “Add the potentials of two charges as vectors.” Repair Potential is a scalar: add the values with their signs. It is the fields that add as vectors.
• “The field points from low potential to high.” Repair E = −ΔV/Δx: the field points from high to low potential, the direction in which V decreases.
• “Electric potential energy is always negative.” Repair Positive for like charges (work was done pushing them together), negative for unlike charges (a bound pair). Only gravitational EP is always negative.
• “Use 9.0 × 109 for 1/(4πε0).” Repair The Data sheet gives 8.99 × 109 m F−1 (and ε0 = 8.85 × 10−12 F m−1). Use the printed value, so a three-figure answer is not thrown off in its last figure.

• Read the command word before you decide how much to write. This syllabus has fifteen of them: calculate, comment, compare, define, describe, determine, explain, give, identify, justify, predict, show (that), sketch, state and suggest. Define wants a precise meaning — for a physical quantity, usually an equation in words with every quantity named. State and give want a fact and nothing more. Describe wants the points or the features. Explain wants the reasons and the relationships — a describe-level answer to an explain question is incomplete however well written it is. Show (that) gives you the result and asks for the structured evidence that leads to it, so every step must appear — and a final value worked to one more significant figure than the one printed makes it plain that you calculated it rather than copied it. Sketch wants a freehand graph with its key features — intercepts, asymptotes, the shape — correct, but no plotted scale.
• Interleave with the chapters that use this one. At chapter 19, re-answer: what is the field between the plates of a capacitor, and what is the potential of an isolated charged sphere? At chapter 20, re-answer: how does the path of a charge in a uniform electric field differ from its path in a uniform magnetic field? At chapter 22, re-answer: how much energy does an electron gain falling through a p.d. V? Recalling a topic inside a new context is worth more than another pass over this chapter on its own; at A Level, Paper 4 assumes the whole of the AS content, so nothing here is ever finished with.

• Cambridge International AS & A Level Physics 9702 has five components. Topic 18 is A Level content, so it is examined in Papers 4 and 5. A Level content: examined in Paper 4 (A Level structured, which also requires the AS content) and, as practical context, Paper 5. AS Level candidates take Papers 1, 2 and 3; A Level candidates take all five, either staged over two years (Papers 1–3 in year one, Papers 4 and 5 in year two) or together in one series. Examinations are available in the June and November series, and in March in India.
• Across both the AS Level and the A Level the assessment objectives are weighted AO1 40% (knowledge and understanding), AO2 40% (handling, applying and evaluating information) and AO3 20% (experimental skills and investigations). AS candidates are graded a–e; A Level candidates A*–E. The Data and formulas sheet is printed as page 2 of Papers 1 and 2 and as pages 2 and 3 of Paper 4: it gives the constants and a short list of formulas. Every other equation in this chapter is one the syllabus says you must recall, and this chapter says which is which.
• There is no multiple-choice paper on A Level content. A Paper 4 question on this topic can ask you to define electric field strength or electric potential, sketch a field-line or equipotential pattern, describe and explain the path of a charged particle between plates, explain why a potential or a potential energy is positive or negative, or compare electric and gravitational fields.
• Calculations with \(F = qE\), \(E = \Delta V/\Delta d\), Coulomb's law and \(E = Q/(4\pi\varepsilon_0 r^2)\), all recall; with \(V = Q/(4\pi\varepsilon_0 r)\) and \(E_\mathrm{P} = Qq/(4\pi\varepsilon_0 r)\), both given. Deflection between plates by the projectile method; fields added as vectors, potentials as scalars; E read from the gradient of a V–x or V–r graph.
• As a Paper 5 context: potential against distance between two electrodes on resistive paper, measured with a digital voltmeter and a probe, whose straight V–x graph gives E from its gradient; or force against separation for two charged spheres, analysed on a lg–lg graph to test the power −2. Probe contact and charge leakage are the uncertainties to name.
• Read the command word before you decide how much to write. This syllabus has fifteen of them: calculate, comment, compare, define, describe, determine, explain, give, identify, justify, predict, show (that), sketch, state and suggest. Define wants a precise meaning — for a physical quantity, usually an equation in words with every quantity named. State and give want a fact and nothing more. Describe wants the points or the features. Explain wants the reasons and the relationships — a describe-level answer to an explain question is incomplete however well written it is. Show (that) gives you the result and asks for the structured evidence that leads to it, so every step must appear — and a final value worked to one more significant figure than the one printed makes it plain that you calculated it rather than copied it. Sketch wants a freehand graph with its key features — intercepts, asymptotes, the shape — correct, but no plotted scale.