Magnetic fields — OCR A-Level Physics
Test yourself on Magnetic fields with OCR A-Level practice questions.
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Magnetic fields explained
A magnetic field is a region where a magnetic force acts on magnetic materials or moving charges.
Read the full explanation
This statement identifies two independent origins. First, moving charges: any current in a wire is a flow of charge, so a current-carrying conductor is surrounded by a magnetic field; a single charge moving through space also produces one. Second, permanent magnets: in iron, cobalt and nickel, atomic magnetic moments align to give a net field without any external current. The two origins are linked, because magnetism in materials arises from moving charges at atomic scale. A useful test is to ask whether a current or a magnetised material is present. Field strength falls with distance from the source, and the field direction depends on current direction or on the orientation of the magnet's poles.
(b) magnetic field lines to map magnetic fields
Magnetic field lines are a visual convention for mapping a magnetic field. The direction of the line at any point gives the direction of the force on a small free north pole placed there, so lines emerge from a north pole and enter a south pole outside a magnet. The spacing of the lines represents field strength: closely spaced lines mean a strong field, widely spaced lines a weak field. Lines never cross, because the field has only one direction at each point. A uniform field is drawn as equally spaced parallel straight lines, for example between the poles of a large horseshoe magnet. Field lines are continuous closed loops; inside a magnet they run from south to north, completing the loop.
(c) magnetic field patterns for a long straight current- carrying conductor, a flat coil and a long solenoid
Each current-carrying shape produces a characteristic field pattern. A long straight conductor gives concentric circles around the wire, with direction from the right-hand grip rule and strength decreasing with distance. A flat coil, such as a circular loop, gives a field through the centre perpendicular to the coil plane, with the two faces acting like north and south poles. A long solenoid gives a nearly uniform field inside along its axis, with field lines outside resembling those of a bar magnet. The solenoid field strength increases with current and with number of turns per unit length. Recognising these patterns allows prediction of field direction and relative strength in each case.
(d) Fleming’s left-hand rule
Fleming's left-hand rule predicts the direction of the force on a current-carrying conductor placed in an external magnetic field. Hold the left hand with the thumb, first finger and second finger mutually perpendicular. The first finger points in the direction of the magnetic field, the second finger in the direction of conventional current, and the thumb gives the direction of the force, also called the motor effect force. The rule applies when the current is not parallel to the field; if current and field are parallel, the force is zero. The force direction is reversed if either the current direction or the field direction is reversed. This rule is used for motors and for charged particles treated as conventional current.
(e)
Statement (e) covers the magnetic force on a current-carrying conductor in an external magnetic field. A wire of length $L$ carrying a current $I$ in a magnetic field of flux density $B$ experiences a force $F$. This is quantified by $F = BIL \sin\theta$, where $\theta$ is the angle between the conductor and the magnetic field lines. The force is maximised when the wire is perpendicular to the field ($\theta = 90^\circ$, giving $F = BIL$). If the wire is parallel to the field ($\theta = 0^\circ$), it experiences zero force. For example, a 0.50 m wire carrying 2.0 A at $30^\circ$ to a 0.10 T field experiences a force of $0.10 \times 2.0 \times 0.50 \times \sin 30^\circ = 0.050$ N. The force direction is always perpendicular to both the current and the magnetic field.
(i) force on a current-carrying conductor; F = ILB sin θ
A straight conductor carrying current I in a uniform magnetic flux density B experiences a force F given by F = ILB sin θ, where L is the length of conductor within the field and θ is the angle between the current direction and the magnetic field lines. The force is greatest when the conductor is perpendicular to the field (θ = 90°, sin θ = 1) and zero when it lies parallel to the field (θ = 0°, sin θ = 0). The force direction is given by Fleming's left-hand rule. For example, a 0.20 m wire carrying 3.0 A at 90° to a 0.50 T field feels F = 3.0 × 0.20 × 0.50 × 1 = 0.30 N. If the wire were at 30°, F = 3.0 × 0.20 × 0.50 × sin 30° = 0.15 N.
(ii) techniques and procedures used to determine the uniform magnetic flux density between the poles of a magnet using a current-carrying wire and digital balance
To measure the flux density between the poles of a magnet, mount a rigid straight wire horizontally between the poles so it is perpendicular to the field, and support the magnet on a digital balance. With no current, record the balance reading. Pass a known current I through the wire and record the new reading; the change in reading gives the force F on the wire (using the balance's force reading, F = mg where needed). Measure the length L of wire between the poles. Since the wire is perpendicular to the field, F = ILB, so B = F / (IL). Repeat for several currents and plot F against I; the gradient is LB, so B = gradient / L. This averages random errors and improves reliability.
(f) magnetic flux density; the unit tesla.
Magnetic flux density B describes the strength of a magnetic field: it is the force per unit current per unit length on a conductor placed at right angles to the field, so B = F / (IL). The SI unit is the tesla (T). One tesla is the flux density that produces a force of 1 newton on a 1 metre length of conductor carrying a current of 1 ampere perpendicular to the field, so 1 T = 1 N A⁻¹ m⁻¹. For example, a field of 0.50 T acting on a 2.0 m wire carrying 4.0 A at 90° gives F = 4.0 × 2.0 × 0.50 = 4.0 N. Flux density is a vector quantity, with direction given by the field lines.
Your focus
- State that magnetic fields arise from moving charges or permanent magnets.
- Distinguish between a stationary charge and a moving charge in terms of magnetic field production.
- Describe how aligned atomic magnetic moments in a permanent magnet produce a net magnetic field.
Show all 24 objectives
- Describe how magnetic field lines represent the direction and relative strength of a magnetic field.
- Identify from a diagram whether a magnetic field is uniform or non-uniform.
- Explain why magnetic field lines cannot cross.
- Describe the magnetic field pattern around a long straight current-carrying conductor.
- Describe the magnetic field pattern produced by a flat coil and by a long solenoid.
- Apply the right-hand grip rule to determine field direction.
- State Fleming's left-hand rule and identify what each finger represents.
- Use Fleming's left-hand rule to determine the direction of the force on a current-carrying conductor.
- Explain why no force acts when the current is parallel to the magnetic field.
- Calculate the force on a current-carrying conductor using the equation $F = BIL \sin\theta$.
- Identify the correct angle $\theta$ between the conductor and the magnetic field lines.
- Explain the conditions under which the magnetic force on a conductor is maximised or zero.
- Recall and rearrange F = ILB sin θ.
- Determine the direction of the force using Fleming's left-hand rule.
- Calculate the force for a conductor at any angle to a uniform magnetic field.
- Describe the apparatus and procedure for measuring flux density with a wire and digital balance.
- Derive and use B = F / (IL) from the force equation.
- Analyse an F–I graph to determine flux density and explain how repeats improve reliability.
- Define magnetic flux density and state its unit, the tesla.
- Express the tesla in base SI units as N A⁻¹ m⁻¹.
- Use B = F / (IL) to calculate flux density for a perpendicular conductor.
Magnetic fields exam tips
Marking Points
- Moving charges produce a magnetic field; a steady current is a flow of charge and so creates a field around the conductor.
- A single charge moving with velocity v produces a magnetic field; a stationary charge does not.
- Permanent magnets produce a magnetic field because atomic magnetic moments within domains are aligned.
- Magnetic materials include iron, cobalt and nickel; alignment of domains gives a net magnetic field.
- The field direction depends on the direction of conventional current or on the orientation of the magnet.
- Field strength decreases with distance from the current or magnet.
- Field lines show the direction of the force on a small free north pole at each point.
- Outside a magnet, field lines run from north pole to south pole; inside, they run from south to north.
- Line spacing indicates field strength: closer lines mean a stronger field.
- Field lines never cross, because the field direction at a point is unique.
- A uniform field is represented by equally spaced parallel straight lines.
- Field lines form continuous closed loops.
- A long straight conductor produces concentric circular field lines around the wire.
- The right-hand grip rule gives the field direction: thumb along conventional current, fingers curl in the field direction.
- A flat coil produces a field through its centre perpendicular to the plane of the coil, with opposite faces acting as north and south poles.
- A long solenoid produces a strong, nearly uniform field inside along its axis.
- Outside a solenoid the field pattern resembles that of a bar magnet.
- Solenoid field strength increases with current and with the number of turns per unit length.
- Fleming's left-hand rule gives the direction of the force on a current-carrying conductor in a magnetic field.
- The first finger points in the direction of the magnetic field.
- The second finger points in the direction of conventional current.
- The thumb gives the direction of the force on the conductor.
- The three directions are mutually perpendicular.
- If the current is parallel to the field, the force is zero.
- State the equation F = ILB sin θ and identify each symbol with its unit: F in newtons (N), I in amperes (A), L in metres (m), B in tesla (T).
- Explain that θ is the angle between the current direction and the magnetic field lines, so the force is maximum at 90° and zero at 0°.
- Apply Fleming's left-hand rule to determine the direction of the force on the conductor.
- Substitute values correctly, including taking sin θ, and give the force with the correct unit and sensible significant figures.
- Describe the apparatus: a straight wire clamped perpendicular to the field between the poles of a magnet, with the magnet resting on a digital balance.
- Explain that the change in balance reading when current flows gives the magnetic force on the wire.
- Measure the length L of wire within the field and the current I, then use B = F / (IL) because the wire is perpendicular to the field.
- Repeat for several values of current and plot a graph of force against current; the gradient equals LB, so B = gradient / L, reducing random error.
- Define magnetic flux density as the force per unit current per unit length on a conductor perpendicular to the field, B = F / (IL).
- State that the SI unit is the tesla (T) and express it as 1 T = 1 N A⁻¹ m⁻¹.
- Explain that flux density is a vector quantity whose direction is the direction of the magnetic field lines.
- Use B = F / (IL) to calculate flux density or force, ensuring the conductor is perpendicular to the field.
Examiner Tips
- 💡Read the stem carefully to identify whether the source is a current, a moving charge or a permanent magnet before choosing an option.
- 💡Eliminate options that describe a stationary charge producing a magnetic field, since that is impossible.
- 💡Check the direction wording: conventional current direction is opposite to electron flow, so field direction follows conventional current.
- 💡Where an option mentions field strength, ask whether it correctly states that the field weakens with distance.
- 💡When asked to interpret a field diagram, check direction arrows first, then spacing, then whether lines cross.
- 💡Use the rule that lines point away from north and towards south outside the magnet.
- 💡For uniform-field questions, look for equally spaced parallel lines rather than curved ones.
- 💡Remember that line density is a qualitative indicator of field strength, not a numerical value.
- 💡Sketch the pattern first, then add arrows using the right-hand grip rule for the straight wire.
- 💡For a solenoid, compare the inside field to a uniform field and the outside field to a bar magnet.
- 💡Check whether the question asks about direction, shape or relative strength before selecting an option.
- 💡Remember that field strength falls with distance from a straight wire but is nearly uniform inside a long solenoid.
- 💡Set up your hand physically before answering, keeping the three directions mutually perpendicular.
- 💡Identify which finger represents field, current and force before reading the options.
- 💡If the question mentions electron flow, convert to conventional current direction first.
- 💡Check whether the current is parallel to the field, because then the force is zero.
- 💡When calculating the force, explicitly state the value of $\sin\theta$; if the wire is perpendicular, write $\sin 90^\circ = 1$ to show your working clearly.
- 💡Remember that $L$ refers only to the length of the conductor that is actually situated within the magnetic field, not the total length of the wire.
- 💡If a question states the wire is parallel to the magnetic field, immediately recognise that the force is zero without needing further calculation.
- 💡Sketch the field lines and the current arrow before substituting, so θ is unambiguous.
- 💡Check that L is the length of conductor inside the field, not the whole wire.
- 💡Give the force in newtons and round to the significant figures justified by the data.
- 💡State clearly that the balance reading changes by the magnetic force, and explain how you isolate that change.
- 💡Describe taking repeat readings and plotting a graph to improve reliability.
- 💡Include the equation B = F / (IL) and show how the gradient of an F–I graph gives LB.
- 💡Learn the defining equation B = F / (IL) and the unit equivalence 1 T = 1 N A⁻¹ m⁻¹.
- 💡Check that the conductor is perpendicular to the field before using B = F / (IL).
- 💡State the direction of B when a question asks about the vector nature of the field.
Common Mistakes
- Thinking a stationary charge produces a magnetic field: the charge must be moving, so a stationary charge has an electric field but no magnetic field.
- Believing permanent magnets contain no moving charge: magnetism in materials arises from atomic-scale moving charges whose moments are aligned.
- Assuming the field around a current is uniform: it is strongest close to the conductor and weakens with distance.
- Confusing magnetic poles with electric charges: isolated magnetic poles have not been observed, whereas positive and negative charges can exist separately.
- Drawing field lines that cross: this would imply two field directions at one point, which is impossible.
- Thinking field lines start and stop at poles: they are continuous closed loops, running south to north inside the magnet.
- Treating widely spaced lines as a strong field: wide spacing indicates a weak field, while close spacing indicates a strong field.
- Assuming field lines show the path of a moving charge: they show field direction, not the trajectory of a particle.
- Drawing straight field lines around a long straight wire: the lines are concentric circles centred on the wire.
- Reversing the right-hand grip rule: the thumb points along conventional current, not electron flow.
- Thinking the field inside a solenoid is zero: it is strong and nearly uniform along the axis.
- Treating the field of a flat coil as identical to that of a straight wire: the coil produces a field through its centre perpendicular to its plane.
- Using the right hand instead of the left: Fleming's left-hand rule applies to the motor effect force on a current.
- Pointing the second finger along electron flow: it must point along conventional current, opposite to electron flow.
- Assuming a force always exists: if the current is parallel to the magnetic field, the force is zero.
- Forgetting that reversing either the current or the field reverses the force direction.
- Forgetting the $\sin\theta$ term when the wire is not perpendicular to the magnetic field. Correction: always check the angle between the current direction and the magnetic field lines before calculating.
- Using the wrong angle for $\theta$. Correction: ensure $\theta$ is the angle between the wire and the magnetic field lines, not the angle between the wire and the normal to the field.
- Incorrectly converting units before applying the formula. Correction: ensure length $L$ is in metres (m), current $I$ is in amperes (A), and magnetic flux density $B$ is in tesla (T) to yield force in newtons (N).
- Using the angle between the wire and the horizontal instead of the angle between the current and the magnetic field. Correction: θ is always measured between the current direction and the field lines.
- Forgetting the sin θ factor and treating every orientation as perpendicular. Correction: include sin θ, which equals 1 only at 90°.
- Mixing up Fleming's left-hand rule with the right-hand rule for induced current. Correction: use the left hand for the force on a current-carrying conductor in a motor effect.
- Using the total length of the wire instead of the length between the magnet poles. Correction: only the length inside the uniform field contributes to the force.
- Ignoring the zero-current balance reading. Correction: subtract the initial reading so only the magnetic force is used.
- Assuming the wire is perpendicular without checking. Correction: align the wire at 90° to the field lines, or include sin θ if it is not.
- Confusing magnetic flux density with magnetic flux. Correction: flux density B is force per unit current per unit length, while flux is the product of flux density and area.
- Writing the tesla as N A m without negative indices. Correction: the correct form is 1 T = 1 N A⁻¹ m⁻¹.
- Treating flux density as a scalar. Correction: it is a vector, with direction along the field lines.