Describe an experiment to show that a force acts on a current-carrying conductor in a magnetic field, including the effect of reversing: (a) the current (b) the direction of the field

4.5.4 Force on a Current‑Carrying Conductor

Learning Objective

Describe an experiment that demonstrates a force acting on a current‑carrying conductor placed in a magnetic field, and explain how the force changes when (a) the direction of the current is reversed, and (b) the direction of the magnetic field is reversed.

Key Theory

The magnetic force on a straight conductor of length \$L\$ carrying a current \$I\$ in a uniform magnetic field \$\mathbf{B}\$ is given by

\$\mathbf{F}=I\,\mathbf{L}\times\mathbf{B}\$

where \$\mathbf{L}\$ is a vector of magnitude \$L\$ directed along the conventional current. The magnitude of the force is

\$F = I L B \sin\theta\$

with \$\theta\$ the angle between \$\mathbf{L}\$ and \$\mathbf{B}\$. For a conductor placed perpendicular to the field (\$\theta = 90^{\circ}\$), \$F = I L B\$.

Apparatus

• U‑shaped magnet (or a pair of bar magnets) producing a uniform magnetic field between the poles.
• Straight insulated copper wire (length ≈ 0.20 m) mounted on a low‑friction pivot or a lightweight wooden plank.
• Power supply (adjustable DC) with ammeter.
• Switch to control current direction.
• Ruler or measuring scale.
• Clamp or stand to hold the wire horizontally.

Experimental Setup

1. Place the U‑shaped magnet on a flat surface with the poles facing each other, creating a region of uniform magnetic field.
2. Position the straight wire so that it lies horizontally across the gap between the poles, perpendicular to the field lines.
3. Mount the wire on a lightweight pivot that allows it to swing freely in the vertical plane.
4. Connect the wire to the power supply through the ammeter and a switch. Ensure the current direction can be reversed by flipping the switch.

Procedure

1. Close the circuit with the switch in the “forward” position. Record the current \$I\$ from the ammeter.
2. Observe the deflection of the wire. Measure the vertical displacement \$d\$ (or angle) using the ruler.
3. Reverse the current by flipping the switch. Record the new direction of deflection.
4. Return the current to its original direction, then rotate the magnet 180° so that the magnetic field direction is reversed. Record the deflection.
5. Repeat the measurements for at least three different current values (e.g., 0.5 A, 1.0 A, 1.5 A) and tabulate the results.

Observations Table

Explanation of Results

• Effect of current reversal: Reversing the current changes the direction of \$\mathbf{L}\$, so the cross‑product \$\mathbf{L}\times\mathbf{B}\$ reverses. The force therefore acts in the opposite direction, causing the wire to deflect opposite to the original deflection.
• Effect of magnetic‑field reversal: Flipping the magnet reverses \$\mathbf{B}\$. The cross‑product again changes sign, giving a force opposite to that observed with the original field direction.
• Proportionality: The magnitude of the deflection is proportional to \$I\$ (and to \$B\$ and \$L\$), consistent with \$F = I L B\$.

Safety and Precautions

• Do not exceed the current rating of the wire to avoid overheating.
• Keep the power supply voltage low (≤ 5 V) to minimise risk of electric shock.
• Secure the magnet so it does not slip during the experiment.
• Handle the ammeter and connections carefully to avoid loose contacts.

Extension Questions

1. How would the deflection change if the wire were placed at an angle \$\theta\$ to the magnetic field? Use the formula \$F = I L B \sin\theta\$ to predict the outcome.
2. Explain how this principle is used in the operation of a galvanometer.
3. If the length of the conductor is doubled while keeping \$I\$ and \$B\$ constant, what happens to the force?

Summary

The experiment clearly demonstrates that a current‑carrying conductor experiences a magnetic force when placed in a magnetic field. Reversing either the current or the magnetic field reverses the direction of the force, while the magnitude remains proportional to \$I\$, \$L\$, and \$B\$. This relationship underpins many practical devices, such as electric motors and measuring instruments.