HS2 Physics Chapter 5 MAGNETISM AND MATTER : Experiments

 

Experiment: Study of a Magnetic Dipole in a Uniform Magnetic Field

Objective:

To study the behavior of a bar magnet (or magnetic needle) placed in a uniform magnetic field and determine the torque and potential energy associated with different orientations.

Apparatus Required:

• Small bar magnet or magnetic needle

• Uniform magnetic field source (Helmholtz coil or Earth’s magnetic field with orientation aid)

• Stand and pivot for suspension

• Protractor or angle measurement setup

• Stopwatch (if oscillations are to be studied)

• Magnetic field measuring device (optional)

Theory:

A magnetic dipole in a magnetic field experiences a torque given by:

$$\vec{\tau} = \vec{m} \times \vec{B}$$

Where:

• $\vec{m}$ is the magnetic moment of the magnet

• $\vec{B}$ is the magnetic field vector

• $\theta$ is the angle between $\vec{m}$ and $\vec{B}$

The potential energy $U$ of the dipole in the field is:

$$U = -\vec{m} \cdot \vec{B} = -mB \cos \theta$$

This implies:

• Minimum energy when $\theta = 0^\circ$ (aligned)

• Maximum energy when $\theta = 180^\circ$ (anti-aligned)

Procedure:

1. Suspend the bar magnet or magnetic needle freely such that it can rotate in a horizontal plane.

2. Align the setup so the needle/magnet is initially in equilibrium (usually pointing along Earth's magnetic field).

3. Apply an external uniform magnetic field using Helmholtz coils or other means.

4. Vary the orientation of the magnet and measure the angle $\theta$ between the magnetic moment and the magnetic field.

5. Record the torque experienced at various angles using the torque formula.

6. Optionally, allow the magnet to oscillate and measure its oscillation period to indirectly estimate magnetic moment.

Observations:

• Angle $\theta$

• Direction of torque

• Calculated torque $\tau = mB \sin \theta$

• Calculated potential energy $U = -mB \cos \theta$

Result:

The torque and potential energy values confirm the theoretical behavior of a magnetic dipole in a uniform magnetic field.

Precautions:

• Ensure the magnetic field is uniform.

• Eliminate external magnetic interferences.

• Ensure accurate angle measurements.