Force on a current-carrying wire

Practical method

Aim

Investigate how the force on a current-carrying wire depends on current and determine the magnetic flux density B.

Variables

Independent variable: current I
Dependent variable: force F (from the balance reading change)
Control variables: length of wire in the field; the same magnet; wire perpendicular to the field.

Apparatus

• U-shaped magnet on a top-pan balance
• Stiff wire clamped above the balance, through the field
• Variable d.c. supply and ammeter
• Ruler

Method

1. Place the magnet on the balance and zero (tare) the reading.
2. Clamp the wire horizontally between the poles, perpendicular to the field, without touching the magnet.
3. Pass currents from 1.0 A to 5.0 A and record the change in balance reading.
4. Force on the wire is equal and opposite to the force on the magnet: F = Δm × g.
5. Plot F against I: gradient = BL, where L is the length of wire in the field.

Sample results

Length of wire in field L = 0.050 m.

Analysis

F is proportional to I with gradient 2.50 × 10⁻³ N A⁻¹ = BL, so B = \(\dfrac{2.50 \times 10^{-3}}{0.050}\) = 0.050 T.

Uncertainty

The balance reads to 0.001 g; at 1.0 A this is 0.4%. The length of wire in the field is uncertain because the field spreads beyond the poles (about ±2 mm in 50 mm, 4%) — the largest uncertainty.

Errors and improvements

Risk assessment

Common mistakes

• Forgetting to convert grams to newtons.
• Using the whole wire length rather than the length in the field.
• Not taring the balance.

Worked analysis

At 4.0 A, Δm = 1.019 g, so F = 1.019 × 10⁻³ × 9.81 = 1.00 × 10⁻² N. B = \(\dfrac{F}{IL}\) = \(\dfrac{0.0100}{4.0 \times 0.050}\) = 0.050 T.

Common misconception

The balance reading changes because of Newton's third law: the magnet experiences an equal and opposite force to the wire.