Required practicals › Force on a current-carrying wire

REQUIRED PRACTICAL 10

Force on a current-carrying wire

Using a top-pan balance to measure how the force on a wire depends on the magnetic flux density, the current and the length in the field.

Theory: Magnetic flux density and the force on a wire

What you are trying to do

Measure the force on a current-carrying wire in a magnetic field with a top-pan balance, and test F = BIl.

Apparatus

  • A pair of magnadur magnets on an iron yoke, standing on a top-pan balance reading to 0.01 g
  • A stiff copper wire clamped rigidly so it passes horizontally between the poles without touching them
  • DC supply, ammeter and rheostat; a switch
  • A rule to measure the length of the magnet region

Variables

  • Independent: the current in the wire
  • Dependent: the force, read as the change in the balance reading
  • Control: the field (same magnets), the length in the field, and the geometry: wire horizontal and at right angles to the field

Method

Required practical 10: the wire is pushed up, so by Newton's third law the magnet is pushed down, and the balance reads moretop-pan balancemagnetIforce on wire: upequal force onmagnet: downreading rises by F/g
FIG. 1The arrangement: the wire is clamped and cannot move, so the force on it is read through its Newton's-third-law partner, the equal and opposite force pressing on the magnets and the balance.
  1. Zero (tare) the balance with the wire in place and the current off.
  2. Switch on, read the change in the balance reading, switch off. Repeat at a series of currents, and reverse the current once to see the reading change sign.
A current-carrying wire in a magnetic field feels a force at right angles to both: F = BIl, by Fleming's left handB into pagecurrent Iforce Fwire length l in the fieldF = BIl, when field and current are perpendicular
FIG. 2The law under test. Maximum force needs the wire perpendicular to the field; the geometry is part of the method, not a detail.
  1. Measure the length of wire actually inside the field: the magnet length, since the field falls away quickly beyond the poles.

Analysis

  1. The balance reads mass, so convert: F = Δm × g, with Δm in kilograms.
  2. Plot F against I. The line through the origin has gradient Bl, so the flux density is the gradient divided by the measured length.

A worked set of readings

Magnadur pair of length 5.0 cm; balance tared at zero current:

I / ABalance change / gF / mN
1.00.414.0
2.00.828.0
3.01.2212.0
4.01.6316.0
5.02.0420.0

The gradient of F against I is 4.0 mN A⁻¹, which is Bl. Dividing by l = 0.050 m gives B = 0.080 T, a typical magnadur field.

Where the uncertainty comes from

  • The field's edges: The field is not a sharp box: it fringes beyond the magnets, so the effective length is slightly more than the magnet length. This is usually the dominant systematic.
  • Balance resolution: 0.01 g is a tenth of a millinewton; small currents produce changes only a few times that, so the graph leans on the larger currents.
  • Geometry: The force falls with the sine of the angle between wire and field; clamp the wire square and horizontal.
  • Heating: Amps through a thin wire warm it; switch off between readings.

What earns the marks

  • The Newton's third law sentence: the balance reads the force on the magnets, equal and opposite to the force on the wire. Examiners ask exactly this.
  • Convert the balance change to newtons with g, in SI units.
  • Gradient of F against I is Bl; divide by l for B.
  • Reversing the current reverses the deflection, which confirms the reading is magnetic and not thermal.

Safety

Currents of several amps heat the wire and drain supplies: switch on only to read. Keep the balance and yoke stable, and keep steel objects away from the magnets.

Method and analysis here follow the standard approach; your school may vary the apparatus. Always follow your teacher’s risk assessment in the lab.