HS2 Physics Chapter 4 MOVING CHARGES AND MAGNETISM : Experiments

 

Experiment: Determination of the Horizontal Component of Earth's Magnetic Field (Bh)

Objective:

To determine the horizontal component of Earth’s magnetic field using a tangent galvanometer.

Apparatus Required:

• Tangent galvanometer

• Ammeter

• Rheostat

• Key

• Battery (or power supply)

• Connecting wires

• A compass box (mounted at the center of the galvanometer)

Theory:

When current passes through the circular coil of the tangent galvanometer, it produces a magnetic field at the center. This field is perpendicular to the plane of the coil. The deflection of the magnetic needle in the compass box at the center is due to the resultant of this magnetic field and the horizontal component of Earth's magnetic field.

Using the tangent law:

$$B = B_h \tan \theta$$

Where:

• $B$ = Magnetic field due to current

• $B_h$ = Horizontal component of Earth's magnetic field

• $\theta$ = Deflection of the needle

Also,

$$B = \frac{\mu_0 n I}{2R}$$

Where:

• $\mu_0$ = Permeability of free space

• $n$ = Number of turns in the coil

• $I$ = Current through the coil

• $R$ = Radius of the coil

From this, we can derive:

$$B_h = \frac{\mu_0 n I}{2R \tan \theta}$$

Procedure:

1. Set up the tangent galvanometer with its plane in the magnetic meridian (i.e., the needle should point in the N-S direction when no current flows).

2. Connect the circuit as per the diagram (battery, key, ammeter, rheostat, and tangent galvanometer in series).

3. Adjust the rheostat to vary the current and note the deflection angle $\theta$ from the compass needle.

4. Record the current from the ammeter for different values of deflection (preferably 30°, 45°, 60°).

5. Calculate $B_h$ using the tangent law.

Precautions:

• The plane of the coil must lie exactly in the magnetic meridian.

• Avoid any nearby magnetic materials.

• Take readings in both directions of current to eliminate errors due to magnetic field asymmetry.

Result:

The horizontal component of Earth’s magnetic field $B_h$ is calculated using the measured deflection angles and current values.