Required Practical 11 — Force on a Current-Carrying Wire

Required Practical 11 (RP11) in the AQA A-Level Physics specification investigates the force on a current-carrying conductor in a magnetic field. The experiment lets you confirm F = BIL by measuring the apparent mass change on a top-pan balance as the current through a wire (suspended between magnet poles) is varied. A linear F-vs-I graph, with the gradient interpreted as BL, gives a direct measurement of the magnetic flux density B between the poles. AQA specification 3.7.5 expects you to describe the procedure, analyse the data quantitatively, evaluate uncertainties, and meet the CPAC practical-endorsement competencies.

Spec mapping: AQA 7408 A-Level Physics, Required Practical 11 (within Section 3.7.5 — Magnetic fields). This lesson covers the standard top-pan-balance setup, the experimental procedure for varying I and recording the mass change Δm, the graphical analysis F = BIL → gradient = BL, the secondary experiment varying L with I held constant, and uncertainty analysis covering balance resolution, ammeter precision, length measurement, and alignment errors. CPAC competencies for the practical endorsement are addressed in context. Refer to the official AQA 7408 specification document for the authoritative wording.

Synoptic links: (i) Forces and equilibrium (3.4) — the balance reads the change in apparent weight (Δm × g) caused by the magnetic force; Newton's third law guarantees that the upward magnetic force on the wire produces an equal-and-opposite downward force on the magnet system, which the balance reads. (ii) Ohm's law and circuit measurement (3.5.1) — the current through the wire is controlled by a variable-resistance power supply or a rheostat, and measured with an ammeter; circuit-design competence is integral to the practical. (iii) Uncertainty analysis (3.1 / RP transferable skills) — RP11 is a standard exemplar for percentage-uncertainty calculations, error bars on graphs, and the gradient-uncertainty technique using min/max lines.

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The Physics Behind the Experiment

When a straight conductor of length L carrying a steady current I sits in a uniform magnetic field of flux density B, with the current direction perpendicular to the field, the conductor experiences a force:

F = BIL

By Newton's third law, if the magnet is sitting on a balance and the wire is held above it, the wire pushes down on the magnet with an equal and opposite reaction force. The balance therefore reads an increase (or decrease, depending on current direction) in apparent mass when the current flows. Converting reading to force:

Δm × g = F = BIL

where Δm is the change in the balance reading (in kg) when the current is switched on, and g = 9.81 N kg⁻¹.

Rearranging for B:

B = Δm × g / (I × L)

Or, by plotting F = Δm × g against I (with L held constant), the gradient of the resulting line is BL, from which B can be extracted given the measured wire length L.

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Equipment and Setup

The standard RP11 apparatus consists of:

1. U-shaped permanent magnet (or two bar magnets clamped with opposing poles facing each other) creating a roughly uniform field in the air gap between the poles. Typical B between school-lab magnet poles is 0.05–0.10 T.
2. Top-pan electronic balance with at least 0.01 g (0.1 mg ideal) resolution, on which the magnet is placed.
3. Clamped rigid copper or brass wire held horizontally between the magnet poles, perpendicular to the field direction. The wire is part of an external circuit, isolated from the balance.
4. Variable DC power supply (typically 0–12 V, with current limiter) or a low-voltage supply with a rheostat in series to control the current.
5. Ammeter measuring the current through the wire (typically 0–5 A on the low-current range).
6. Ruler measuring the length L of the wire that lies within the magnetic field (i.e., between the magnet pole-pieces, not the total length of the wire in the circuit).

graph TD
    A["Power supply (DC, variable)"] --> B["Rheostat"]
    B --> C["Ammeter"]
    C --> D["Horizontal wire<br/>(in magnet gap)"]
    D --> E["Return to power supply"]
    F["U-magnet on balance pan"] --> G["Wire passes through gap<br/>perpendicular to B"]
    G --> H["Read Δm on balance<br/>when I flows"]

    style F fill:#3498db,color:#fff
    style H fill:#27ae60,color:#fff

Setup Diagram (Described)

A U-shaped magnet sits on the pan of a digital electronic balance. The N and S poles face each other horizontally with a gap of ~2–3 cm. A stiff horizontal copper wire is clamped at both ends (well outside the magnet, so the clamps do not interact with the balance) and passes through the gap, perpendicular to the line joining the poles. The wire is connected via flexible leads to a power supply, ammeter and rheostat. When current flows along the wire, the magnetic force on the wire is vertical (up or down depending on current direction); the reaction force on the magnet is equal and opposite, and the balance reading changes by Δm = F/g.

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Experimental Procedure

Part A — Investigating F vs I (L constant)

1. Zero the balance with the magnet on the pan and the wire in position but no current flowing. The balance reading should be steady at zero (or note the unloaded reading to subtract from subsequent values).

2. Measure the wire length L in the field. This is the length of wire between the inner faces of the two pole-pieces, where the field is roughly uniform. Use a ruler with mm resolution.

3. Connect the circuit with the rheostat at maximum resistance (minimum current). Switch on the power supply.

4. Adjust the rheostat to give a current of 0.5 A. Record the current I from the ammeter and the change in balance reading Δm from the balance.

5. Repeat for currents of 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0 A (at least 6 distinct values, ideally 8–10). Record I and Δm at each.

6. Plot Δm × g (force) on the y-axis against I on the x-axis. The graph should be a straight line through the origin, with gradient BL.

7. Calculate B from the gradient: B = gradient / L.

Part B — Investigating F vs L (I constant)

A second confirmation can be obtained by varying the length L of wire in the field, with I held at a fixed value:

1. Hold the current at a fixed value (e.g., I = 3.0 A) using the rheostat.

2. Replace the standard wire arrangement with a series of wires of different lengths in the magnet gap, e.g. by using a sliding pair of magnet pole-pieces to vary the effective L from 1.0 to 5.0 cm.

3. Record Δm at each value of L.

4. Plot F = Δm × g against L. The gradient should be BI, from which B = gradient / I.

Comparing the value of B from Part A and Part B is a useful internal consistency check.

Worked Example 1 — Calculating B from RP11 Data

Question: A student records the following data with a wire of length L = 4.0 cm in the magnet gap:

I (A)	Δm (g)
0.50	0.10
1.00	0.20
1.50	0.31
2.00	0.40
2.50	0.51
3.00	0.61

Calculate F at each current, plot F vs I, find the gradient, and calculate B.

Solution:

F = Δm × g, with g = 9.81 m s⁻²:

I (A)	Δm (g)	Δm (kg)	F (N)
0.50	0.10	1.0 × 10⁻⁴	9.81 × 10⁻⁴
1.00	0.20	2.0 × 10⁻⁴	1.962 × 10⁻³
1.50	0.31	3.1 × 10⁻⁴	3.041 × 10⁻³
2.00	0.40	4.0 × 10⁻⁴	3.924 × 10⁻³
2.50	0.51	5.1 × 10⁻⁴	5.003 × 10⁻³
3.00	0.61	6.1 × 10⁻⁴	5.984 × 10⁻³

Gradient (BL) ≈ (5.984 × 10⁻³ − 9.81 × 10⁻⁴) / (3.00 − 0.50) = 5.003 × 10⁻³ / 2.50 ≈ 2.00 × 10⁻³ N A⁻¹

B = gradient / L = 2.00 × 10⁻³ / 0.040 = 0.050 T = 50 mT

This is a typical value for a small school-lab U-magnet.

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Uncertainty Analysis

A careful RP11 report includes percentage uncertainties for each measured quantity and a propagation to the final B value.

Uncertainty in Δm (balance resolution)

A typical electronic balance with 0.01 g resolution has an absolute uncertainty in each reading of ±0.005 g (half the smallest division). For a Δm reading of 0.50 g, the percentage uncertainty is:

(0.005 / 0.50) × 100% = 1.0%

For smaller readings (e.g., Δm = 0.10 g at the lowest current), the percentage uncertainty rises to 5%. This argues for working at currents that give substantial Δm — but not so large that the wire overheats.

Uncertainty in I (ammeter precision)

A digital ammeter typically reads ±0.01 A on the lower current range. For I = 3.00 A, the percentage uncertainty is:

(0.01 / 3.00) × 100% = 0.3%

This is small and usually negligible compared to the balance uncertainty.

Uncertainty in L (length measurement)

A ruler with 1 mm resolution has uncertainty ±0.5 mm in each reading; if you measure both ends, the combined uncertainty is ±1 mm. For L = 4.0 cm = 40 mm, the percentage uncertainty is:

(1 / 40) × 100% = 2.5%

This is often the dominant uncertainty in RP11, because the "active length" of wire in the field is not sharply defined — the field falls off gradually at the edges of the pole-pieces, and what counts as L is a matter of judgement. Some students report L with a deliberately large uncertainty (e.g., ±2 mm) to reflect this ambiguity.

Combining Uncertainties

For B = gradient / L = (Δm × g) / (I × L) — assuming g is exact — the percentage uncertainties add in quadrature (or, for an A-Level approximation, simply add):

% unc. in B ≈ % unc. in Δm + % unc. in I + % unc. in L ≈ 1.0% + 0.3% + 2.5% = 3.8%

For B = 0.050 T, this gives an absolute uncertainty of 0.050 × 0.038 = 0.002 T, so the result is reported as B = (0.050 ± 0.002) T or B = (50 ± 2) mT.

Worked Example 2 — Uncertainty Propagation

Question: From the gradient analysis above, B was found to be 0.050 T. If the percentage uncertainties are ±2% in the gradient and ±2.5% in L, calculate the absolute uncertainty in B.

Solution:

% unc. in B ≈ 2% + 2.5% = 4.5%

Absolute unc. = 0.045 × 0.050 = 0.00225 T ≈ 0.002 T

B = (0.050 ± 0.002) T

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CPAC Competencies for RP11

The Common Practical Assessment Criteria (CPAC) for the practical endorsement require demonstration of five competencies. RP11 is an excellent context for demonstrating each.

CPAC 1 — Follows written procedure: Set up the circuit, attach the wire correctly, balance the magnet on the pan, take readings systematically at increasing currents.

CPAC 2 — Applies investigative approaches and methods: Choose appropriate current range, decide on the number of repeats, decide on the value of L to use, plan the order of variables to control.

CPAC 3 — Safely uses range of practical equipment and materials: Use the power supply within rated current; do not let the wire overheat; switch off between readings to avoid drift; ensure ammeter is connected in series and within range.

CPAC 4 — Makes and records observations: Record I and Δm to appropriate precision; note ammeter range and balance resolution; identify systematic errors (e.g., wire not exactly perpendicular to B).

CPAC 5 — Researches, references and reports: Cite the source of the formula F = BIL (Fleming, motor effect); reference textbook values of B for similar magnets; present results with appropriate uncertainty and significant figures.

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Sources of Systematic Error

Several systematic errors can bias the measured value of B.

1. Wire not exactly perpendicular to B — if the angle differs from 90° by even 10°, the effective force is reduced by sin(80°) = 0.985, a 1.5% reduction. Always sight along the apparatus to check that the wire is straight and perpendicular.

2. Field not uniform across L — at the edges of the pole-pieces, the field strength falls off and the assumption of uniform B becomes invalid. Using a wire shorter than the pole-piece width minimises this effect, but a small bias remains.

3. Balance drift — top-pan balances can drift by a few mg over a few minutes, particularly if the room is draughty or the balance is on an unstable bench. Tare the balance frequently and take readings as quickly as possible without rushing.

4. Magnetic interaction between wire and surroundings — nearby ferromagnetic objects (steel clamps, iron retort stands) can distort the field. Use non-magnetic stands (aluminium or wooden retort stands) where possible.