Magnetic flux density (A-level only) — AQA A-Level Physics

Magnetic flux density (B) is a fundamental concept in electromagnetism that quantifies the strength and direction of a magnetic field. It is defined through the force exerted on a current-carrying conductor (F = BIL sinθ) or a moving charge (F = BQv sinθ), and is measured in tesla (T). Understanding B is essential for analysing motors, generators, and transformers, and it links directly to magnetic flux (Φ) and electromagnetic induction.

In the AQA A-level Physics specification, this topic appears in the 'Fields and their consequences' unit, where students must apply vector rules, use Fleming's left-hand rule, and perform calculations involving angles. It also underpins later topics such as electromagnetic induction, where changing flux density induces an emf (Faraday's law). Mastery of B is crucial for both theoretical understanding and practical problem-solving in exams.

• →Magnetic flux density B is a vector quantity measured in tesla (T), where 1 T = 1 N A⁻¹ m⁻¹.
• →The force on a current-carrying conductor is given by F = BIL sinθ, where θ is the angle between the current and the magnetic field.
• →The force on a moving charge is given by F = BQv sinθ, where θ is the angle between the velocity and the magnetic field.
• →Fleming's left-hand rule predicts the direction of the force on a current-carrying conductor in a magnetic field.
• →Magnetic flux Φ is a scalar quantity measured in webers (Wb), defined as Φ = BA cosθ, and flux linkage is NΦ for a coil of N turns.

• States F = BIl and applies it only when the current is perpendicular to the magnetic field.
• Identifies B as magnetic flux density in tesla, with 1 T = 1 N A⁻¹ m⁻¹.
• Uses Fleming's left-hand rule to determine the direction of the force, which is perpendicular to both field and current.
• Recognises that a wire parallel to the field experiences zero force, and uses the perpendicular component of length for other angles.
• Rearranges the equation to find B, I or l and substitutes consistent SI units.
• Explains that the force arises from the magnetic force on the moving charge carriers in the wire.
• States that the first finger represents the magnetic flux density B, directed from north to south.
• States that the second finger represents conventional current, from positive to negative.
• States that the thumb represents the direction of the force on the conductor.
• Describes the three digits as mutually perpendicular when the hand is held correctly.
• Applies the rule to a moving positive charge by taking the current direction as the velocity direction.
• Applies the rule to a moving negative charge by reversing the current direction relative to the velocity, or by reversing the force direction.
• Recognises that the force is zero when the current is parallel to the magnetic field and maximum when perpendicular.
• Defines magnetic flux density as the force per unit current per unit length on a conductor perpendicular to the field.
• States that the tesla is the unit of magnetic flux density and is equivalent to N A⁻¹ m⁻¹.
• Uses F = BIl for a conductor perpendicular to a uniform magnetic field and rearranges it to find B, F, I or l.
• Explains that the force is maximum when the conductor is perpendicular to B and zero when parallel, using F = BIl sin θ.
• Describes B as a vector whose direction is the direction of the magnetic field from north to south.
• Distinguishes magnetic flux density B from magnetic flux Φ, including the relationship Φ = BA for a uniform perpendicular field.
• Sets up the magnet assembly on the top pan balance with the rigid wire segment horizontal and perpendicular to the magnetic field between the poles.
• Uses the balance reading difference between current on and current off to obtain the magnetic force, recognising the third-law pairing between force on wire and force on magnet.
• Varies one independent variable at a time: current with an ammeter and variable resistor, flux density with different magnet assemblies, length with different wire segments or a tapping jockey.
• Plots a graph of force against the independent variable and interprets a straight line through the origin as direct proportionality, using the gradient to find B, I or l.
• Controls relevant variables, such as keeping the wire perpendicular to the field, keeping the wire in the same region of field, and avoiding heating effects by limiting current.
• Repeats readings and averages to reduce random uncertainty, and considers systematic effects such as the balance zero and the mass of connecting leads.

• 💡Sketch the field, current and force directions with arrows before substituting numbers.
• 💡Convert length to metres and current to amperes, and quote the force in newtons with a sensible number of significant figures.
• 💡If the wire is at an angle, state clearly that you are using the perpendicular component of length.
• 💡Sketch the left hand with labelled fingers beside your working so the examiner can see the direction reasoning clearly.
• 💡When a question gives an electron beam, state explicitly that conventional current is opposite to the electron velocity before applying the rule.
• 💡Check whether the field and current are perpendicular; if they are parallel, state that the force is zero rather than forcing a direction.
• 💡When defining the tesla, specify one newton, one ampere, one metre and perpendicular orientation, because each condition is part of the definition.
• 💡Show the rearrangement of F = BIl before substituting values so that the examiner can follow your method.
• 💡If a question gives an angle, check whether it is measured between the conductor and the field or between the conductor and the normal to the field, and use sin θ only for the angle between conductor and field.
• 💡State clearly that the balance measures the force on the magnet, which is equal and opposite to the force on the wire, and explain how the difference in readings gives F.
• 💡When describing how to vary flux density, refer to changing the magnet assembly or the number of magnets rather than vaguely 'using a stronger magnet'.
• 💡Link each graph shape to the equation F = BIl: force proportional to current and to length at constant B, and proportional to flux density at constant I and l.
• 💡Always write the formula you are using before substituting numbers; this secures method marks even if the final answer is wrong.
• 💡Pay attention to units: convert all lengths to metres, currents to amperes, and angles to degrees or radians as required. The tesla is a derived unit, so show consistency.
• 💡When using Fleming's left-hand rule, describe the direction clearly using words like 'into the page' or 'to the right', and relate it to the field and current directions.

• Using the full length of a wire that is not perpendicular to the field; correct by using the component of length perpendicular to the field, l sin θ.
• Applying F = BIl when the wire is parallel to the field, which gives zero force; correct by checking the angle between current and field first.
• Confusing the direction of force with the direction of current or field; correct by applying Fleming's left-hand rule with the first two fingers mutually perpendicular.
• Using the right hand instead of the left hand: the right-hand rule gives the direction for a generator effect, so use the left hand for the motor effect force.
• Pointing the second finger along electron flow rather than conventional current: conventional current is opposite to electron flow, so reverse the finger for negative charge carriers.
• Treating the first finger as the force and the thumb as the field: the first finger is the field and the thumb is the force, so swap them to obtain the correct prediction.
• Confusing magnetic flux density B with magnetic flux Φ: B is force per unit current per unit length, while Φ is the total field passing through an area, so use Φ = BA to link them.
• Using F = BIl when the conductor is not perpendicular to the field: include sin θ, where θ is the angle between the conductor and the field, so the magnitude of the force is BIl sin θ.
• Writing the unit as N A m⁻¹ without the inverse on the ampere: the correct equivalent unit is N A⁻¹ m⁻¹, because current is divided by in the definition.
• Assuming the balance reading itself equals the magnetic force; the correction is to use the difference between the current-on and current-off readings.
• Leaving the wire at an angle to the field; the correction is to align the wire perpendicular to the field so that the full F = BIl relationship applies.
• Using large currents for long periods; the correction is to keep currents modest and switch off between readings to avoid heating that changes resistance and field conditions.
• Students often think that magnetic flux density and magnetic flux are the same thing. Correction: B is field strength per unit area (vector, tesla), while Φ is the total field through an area (scalar, weber).
• Students may believe that a magnetic field exerts a force on a stationary charge. Correction: A magnetic field only exerts a force on a moving charge or a current-carrying conductor; the force is zero if the charge is stationary or moving parallel to the field.
• Students sometimes forget the sinθ factor when the conductor is not perpendicular to the field. Correction: The force is maximum when θ = 90° and zero when θ = 0° or 180°, so always include sinθ in calculations.

1. 1Day 1-2: Review the definition of magnetic flux density and the formula F = BIL sinθ. Practice simple calculations with varying angles.
2. 2Day 3-4: Learn Fleming's left-hand rule and apply it to determine force directions in different orientations. Draw diagrams for each case.
3. 3Day 5-6: Study the force on a moving charge (F = BQv sinθ) and compare it with the force on a current-carrying conductor. Solve problems involving electrons and protons in magnetic fields.
4. 4Day 7-8: Understand magnetic flux (Φ = BA cosθ) and flux linkage (NΦ). Practice calculations for coils and solenoids.
5. 5Day 9-10: Attempt past paper questions on magnetic flux density, focusing on multi-step problems and explanations. Review mark schemes to identify common pitfalls.

• 📋Calculation of force on a current-carrying conductor: Use F = BIL sinθ, ensuring correct angle and unit conversions. Often combined with Fleming's left-hand rule for direction.
• 📋Calculation of magnetic flux and flux linkage: Use Φ = BA cosθ and NΦ, paying attention to the angle between the field and the normal to the area.
• 📋Explanation of the force on a moving charge: Describe how the force is perpendicular to velocity, leading to circular motion, and calculate radius using r = mv/(BQ).
• 📋Practical-based question: Describe an experiment to determine magnetic flux density, such as using a current balance, and analyse sources of uncertainty.