Force on a current-carrying conductor
Investigate how the force on a current-carrying conductor in a magnetic field depends on current and length.
Apparatus
- Stiff copper wire or conducting rod on a support
- Two magnadur magnets mounted on a steel yoke (uniform magnetic field between poles)
- Electronic balance (milligram resolution)
- Variable DC power supply and ammeter
- Ruler and connecting leads
Safety
- Do not allow high currents to flow for extended periods; the wire heats up and could burn or melt insulation.
- Ensure the magnet yoke is stable on the balance pan.
Method
- Place the magnets on the balance pan so the wire sits horizontally between the poles in the uniform field. Zero the balance with the circuit connected but no current flowing.
- Pass a current I through the wire and record the change in balance reading (in grams); convert to force: $F = m \times g$.
- Vary I in steps from 0.5 A to 4 A. Record F for each current. Plot F vs I (at constant L).
- Repeat with wires of different lengths L between the poles. Plot F vs L at constant I.
- Determine B from the gradient of each graph: F vs I gives gradient $= BL$; F vs L gives gradient $= BI$.
Key Variables
Independent
Current I (then length L)
Dependent
Force F
Controlled
Magnetic flux density B (same magnets, same separation); L when varying I; I when varying L
Analysis and Results
- $F = BIL$: force is proportional to both I and L.
- F vs I (constant L): gradient $= BL$, so $B = \text{gradient}/L$.
- F vs L (constant I): gradient $= BI$, so $B = \text{gradient}/I$.
- Compare B values obtained from both graphs as a consistency check.
Common Errors
- Not zeroing the balance before passing current.
- Measuring the total wire length rather than only the length L within the magnetic field.
- Reversing the current direction unexpectedly, causing the force to act downwards instead of upwards.
- Moving the magnets between measurements, changing B.
Exam-style questions on this practical. Click Show mark scheme to reveal the answer after attempting each question.
Q13 marks
A wire of length 0.12 m carries a current of 3.5 A at right angles to a uniform magnetic field of flux density 0.085 T. Calculate the force on the wire.
Q23 marks
A student plots F against I and obtains a straight line through the origin with gradient 0.018 N A$^{-1}$. The length of wire in the field is 0.15 m. Determine B.
Q32 marks
Explain how the student should orient the wire to ensure $F = BIL$ applies exactly.