Magnetic fields

• Left hand for the force, right hand for the field of a current, and reverse the current finger for an electron. The force is always at 90° to the motion, so it never changes a particle’s speed; only a change of flux linkage induces an e.m.f.
• Left hand for force, right hand for the field of a current, reverse for electrons. Force at 90° to the motion: no work, a circle, r = mv/(BQ). Only a change of flux linkage induces an e.m.f., and it opposes the change.

• 20.1.1 I can understand — understand that a magnetic field is an example of a field of force produced either by moving charges or by permanent magnets
• 20.1.2 I can represent a magnetic field by field lines
• 20.2.1 I can understand — understand that a force might act on a current-carrying conductor placed in a magnetic field
• 20.2.2 I can recall — recall and use the equation F = BIL sin θ, with directions as interpreted by Fleming's left-hand rule
• 20.2.3 I can define — define magnetic flux density as the force acting per unit current per unit length on a wire placed at right-angles to the magnetic field
• 20.3.1 I can determine — determine the direction of the force on a charge moving in a magnetic field
• 20.3.2 I can recall — recall and use F = BQv sin θ
• 20.3.3 I can understand — understand the origin of the Hall voltage and derive and use the expression V_H = BI/(ntq), where t = thickness
• 20.3.4 I can understand — understand the use of a Hall probe to measure magnetic flux density
• 20.3.5 I can describe — describe the motion of a charged particle moving in a uniform magnetic field perpendicular to the direction of motion of the particle
• 20.3.6 I can explain — explain how electric and magnetic fields can be used in velocity selection
• 20.4.1 I can sketch — sketch magnetic field patterns due to the currents in a long straight wire, a flat circular coil and a long solenoid
• 20.4.2 I can understand — understand that the magnetic field due to the current in a solenoid is increased by a ferrous core
• 20.4.3 I can explain — explain the origin of the forces between current-carrying conductors and determine the direction of the forces
• 20.5.1 I can define — define magnetic flux as the product of the magnetic flux density and the cross-sectional area perpendicular to the direction of the magnetic flux density
• 20.5.2 I can recall — recall and use Φ = BA
• 20.5.3 I can understand — understand and use the concept of magnetic flux linkage
• 20.5.4 I can understand — understand and explain experiments that demonstrate: • that a changing magnetic flux can induce an e.m.f. in a circuit • that the induced e.m.f. is in such a direction as to oppose the change producing it • the factors affecting the magnitude of the induced e.m.f.
• 20.5.5 I can recall — recall and use Faraday's and Lenz's laws of electromagnetic induction

Units, significant figures and working are part of the physics. Give a calculated answer to the same number of significant figures as the least precise data, or one more; keep full precision in the working and round only at the end; write the unit with every final answer. A fifth of the qualification is experimental: Papers 3 and 5 test AO3 only, and their questions may be set in contexts outside the syllabus content, so the practical work in this chapter is set out as method, recording, graphs and uncertainties rather than as theory.

• “Use Fleming’s rule to find the direction of the field round a wire.” Correct Left hand for force, right hand for the field of a current, and reverse for electrons. Fleming’s left-hand rule gives the force on a current in a field. The right-hand grip rule gives the field made by a current. For a negative charge, point the current finger opposite to its velocity.
• “A charge in a magnetic field feels a force.” Correct Only a moving charge does, and only if it has a velocity component across the field: \(F = BQv\sin\theta\) is zero when v = 0 and when v is along B. A wire parallel to the field feels no force either.
• “The magnetic force speeds the particle up, like an electric field does.” Correct The magnetic force is always at 90° to the velocity, so it does no work: the speed and kinetic energy stay constant and the path is a circle. A uniform electric field gives a parabola with a changing speed.
• “In \(V_H = BI/(ntq)\), t is the width across which the voltage is measured.” Correct t is the thickness measured along B. The width d across which \(V_H\) appears cancels out of the derivation.
• “There is a formula for the field inside a solenoid.” Correct Not in this syllabus. Topic 20 asks you to sketch the field patterns of a wire, a flat coil and a solenoid, and to use a value of B that a question supplies. No constant for the field of a current appears on the Data sheet.
• “A strong magnet held inside a coil induces a large e.m.f.” Correct A steady flux induces nothing. The e.m.f. equals the rate of change of flux linkage, so it exists only while the flux linkage is changing.
• “The induced current always opposes the magnetic field.” Correct It opposes the change. When the flux through a coil is falling, the induced current makes a field in the same direction as the original one, to try to keep it up.
• “A stationary charge in a magnetic field feels a force.” Repair Only moving charges (and currents) do. \(F = BQv\sin\theta\) is zero when v = 0.
• “Use the right hand for the motor effect.” Repair Fleming’s left-hand rule gives the force; the right-hand grip rule gives the field made by a current.
• “For an electron, point the second finger along its velocity.” Repair The second finger is conventional current, which points opposite to an electron’s velocity. The force on an electron is opposite to the force on a proton moving the same way.
• “Magnetic flux density is the force per unit current per unit length on a wire.” Repair Incomplete: …on a wire placed at right-angles to the magnetic field. At any other angle the force is smaller, so the condition belongs in the definition.
• “In \(F = BIL\sin\theta\), θ is the angle between the force and the field.” Repair The force is always at 90° to the field. θ is the angle between the current (the wire) and the field.
• “The magnetic force speeds the particle up.” Repair It is always perpendicular to v, so it does no work: the speed and kinetic energy stay constant and only the direction changes.
• “A charged particle in a magnetic field follows a parabola.” Repair A circle, when v is perpendicular to a uniform B. The parabola is a uniform electric field.
• “In \(V_H = BI/(ntq)\), t is the width across which \(V_H\) is measured.” Repair t is the thickness along B; the width cancels in the derivation.
• “A velocity selector selects particles by their charge.” Repair \(v = E/B\): q cancels and m never appears, so it selects by speed only.
• “Currents in the same direction repel.” Repair They attract; opposite currents repel. The forces on the two wires are equal and opposite even if the currents differ.
• “A strong steady field through a coil induces a large e.m.f.” Repair Only a changing flux linkage induces an e.m.f.; a steady one, however large, induces none.
• “The induced current always opposes the magnetic field.” Repair It opposes the change. If the flux is falling, the induced field is in the same direction as the original field.

• 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 means give a precise meaning; for a physical quantity, an equation in words with every quantity named does this well. State means express in clear terms, and give means produce an answer from a given source or from memory: a fact, and nothing more. Describe means state the points of a topic, or give its characteristics and main features. Explain means set out purposes or reasons, make the relationships between things clear, say why and/or how, and support with relevant evidence — so a describe-level answer to an explain question is incomplete however well written it is. Show (that) means provide structured evidence that leads to a given result, so every step must appear; working a final value to one more significant figure than the one printed makes it plain that you calculated it rather than copied it. Sketch means make a simple freehand drawing showing the key features: for a graph, the shape, intercepts and asymptotes, with no plotted scale; for a diagram such as a field pattern, the features that matter, such as the direction, shape and spacing of the lines.
• Because the magnetic force on a free particle is always at 90° to its velocity, it never does work. A magnetic field alone can turn a charged particle but can never speed it up or slow it down. Any change of speed in a problem comes from an electric field.
• Two angles, two definitions of θ. In \(F = BIL\sin\theta\) and \(F = BQv\sin\theta\), θ is the angle between the wire (or the velocity) and the field, and the force is greatest at 90°. For flux through a tilted area, use the component of the area perpendicular to the field: the flux is greatest when the plane of the coil is perpendicular to B and zero when it is parallel. Draw the angle before you choose sine or cosine.
• Uncertainty rules used above, from the syllabus. Raw readings of one quantity to the same precision (every Δm to 0.01 g, every I to 0.01 A). Percentage uncertainties add for products and quotients, by simple addition. The uncertainty in a gradient is the difference between the best-fit gradient and the gradient of the worst acceptable line (the steepest or shallowest line through all the error bars). An improvement must be something the apparatus did not already allow, and “take more care” is not a source of uncertainty or an improvement.
• Interleave with the chapters this one stands on. Topic 12 supplies the circle: when you revise circular motion, re-answer “what provides the centripetal force on a charged particle in a magnetic field, and why does its speed never change?” Topic 18 is the other half of the velocity selector and of the Hall field: when you revise it, re-answer “why is the path a parabola there and a circle here?” 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 20 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.
• Structured questions ask you to define magnetic flux density or magnetic flux in the syllabus’s words, state Faraday’s and Lenz’s laws, sketch the field of a wire, coil or solenoid, determine the direction of a force, and explain the origin of the Hall voltage, the circular path of a particle, velocity selection and the forces between wires. There is no multiple-choice paper on A Level content.
• Only the Hall voltage \(V_H = BI/(ntq)\) is printed on the Data and formulas sheet. \(F = BIL\sin\theta\), \(F = BQv\sin\theta\),\(\Phi = BA\) and Faraday’s law are recalled; \(r = mv/(BQ)\) and \(v = E/B\) are worked out each time from a force balance. Constants e, me, mp, u and g come from the Data sheet.
• The current balance measures B from the change in a balance reading as the current is varied: a graph of Δm against I has gradient BL/g. A Hall probe measures B directly and is the instrument in a plan to find how the field of a solenoid depends on its current. Both are set out in the practical-skills section.
• 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 means give a precise meaning; for a physical quantity, an equation in words with every quantity named does this well. State means express in clear terms, and give means produce an answer from a given source or from memory: a fact, and nothing more. Describe means state the points of a topic, or give its characteristics and main features. Explain means set out purposes or reasons, make the relationships between things clear, say why and/or how, and support with relevant evidence — so a describe-level answer to an explain question is incomplete however well written it is. Show (that) means provide structured evidence that leads to a given result, so every step must appear; working a final value to one more significant figure than the one printed makes it plain that you calculated it rather than copied it. Sketch means make a simple freehand drawing showing the key features: for a graph, the shape, intercepts and asymptotes, with no plotted scale; for a diagram such as a field pattern, the features that matter, such as the direction, shape and spacing of the lines.