🧲 Earth's Magnetic Field

Determine Horizontal Component Using Tangent Galvanometer

✅ FREE Experiment • 🧭 Interactive Compass • 🎓 NEB Class 12 Physics

🎯 Introduction

The Earth behaves like a giant bar magnet with magnetic poles near (but not exactly at) the geographic poles. The Earth's magnetic field has two components: a horizontal component (BH) parallel to the Earth's surface, and a vertical component (BV) perpendicular to it. In this experiment, we use a Tangent Galvanometer to measure the horizontal component BH.

A tangent galvanometer consists of a circular coil and a compass needle at its center. When current flows through the coil, it creates a magnetic field perpendicular to Earth's horizontal field. The compass needle, which was initially aligned with Earth's field, deflects by an angle θ. By measuring this deflection and knowing the current, we can calculate BH using the tangent law: BH = B tan(θ).

🎯 Learning Objectives

Interactive Tangent Galvanometer

Experiment Setup

📊 Current Readings

Current (I): 0.5 A
Deflection (θ): 45.0°
tan(θ): 1.000
Field by Coil (B): 0.000 T
BH (Calculated): 0.000 T

Current through circular coil

Turns in the coil

Radius of circular coil

Actual Earth's field (varies by location)

💡 Tip: Align the coil in the magnetic meridian (North-South) before starting. When current flows, the compass needle deflects from North direction.

📊 Calculated Results

Current (I)
0.5
Amperes
Deflection (θ)
45.0
degrees
Coil Field (B)
0.00
×10⁻⁵ T
BH (Measured)
0.00
×10⁻⁵ T
Mean BH
0.00
×10⁻⁵ T
Percentage Error
0.0
%

🧮 Tangent Law Formula

BH = B / tan(θ)

Where B = (μ₀nI) / (2r)

μ₀ = 4π×10⁻⁷ T·m/A, n = turns, I = current (A), r = radius (m), θ = deflection angle

📋 Observation Table

Given: Number of turns n = 10, Radius of coil r = 0.10 m, μ₀ = 4π×10⁻⁷ T·m/A

S.No. Current
I (A)
Deflection
θ (degrees)
tan(θ) Coil Field B
= μ₀nI/(2r) (T)
BH = B/tan(θ)
(T)
No observations recorded yet. Adjust current and click "Record" to add readings

Mean Horizontal Component of Earth's Magnetic Field: Calculate after recording observations

📚 Theory & Concepts

Earth's Magnetic Field

The Earth acts as a huge magnet with its magnetic axis inclined at about 11.5° to the geographic axis (axis of rotation). The magnetic field has three components:

Relationship Between Components

BE² = BH² + BV²
tan(δ) = BV / BH

Where δ is the angle of dip (magnetic inclination)

Tangent Galvanometer Principle

A tangent galvanometer consists of a vertical circular coil with a small magnetic needle (compass) suspended at its center. The coil is placed in the magnetic meridian (North-South direction).

When current flows through the coil:

  1. The coil produces a magnetic field B at its center, perpendicular to its plane (East-West direction)
  2. Earth's horizontal field BH acts along the meridian (North-South)
  3. The compass needle aligns with the resultant of these two perpendicular fields
  4. The deflection angle θ satisfies: tan(θ) = B / BH

Derivation of Tangent Law

Step 1: Magnetic Field at Center of Circular Coil

For a circular coil of radius r carrying current I with n turns:

B = (μ₀nI) / (2r)

Where μ₀ = 4π × 10⁻⁷ T·m/A (permeability of free space)

Step 2: Resultant Field

The compass needle experiences two perpendicular fields:

Resultant field: R = √(BH² + B²)

Step 3: Deflection Angle

The needle aligns with resultant field, making angle θ with BH:

tan(θ) = B / BH

Step 4: Calculate BH

BH = B / tan(θ)
BH = (μ₀nI) / (2r tan(θ))

Important Magnetic Terms

1. Magnetic Meridian

A vertical plane passing through the magnetic north and south poles. A freely suspended magnetic needle aligns itself in this plane. Also called magnetic North-South line.

2. Geographic Meridian

A vertical plane passing through the geographic north and south poles (Earth's axis of rotation). Also called true North-South line.

3. Magnetic Declination (α)

The angle between magnetic meridian and geographic meridian at a place. It varies from place to place and changes with time. In some places it's zero (magnetic and geographic north coincide).

4. Angle of Dip (δ)

The angle made by Earth's total magnetic field with the horizontal direction. At magnetic equator, δ = 0° (field is horizontal). At magnetic poles, δ = 90° (field is vertical).

tan(δ) = BV / BH

Values of Earth's Magnetic Field

Why Tangent Galvanometer for BH?

The tangent galvanometer is specifically designed to measure BH because:

🔬 Experimental Procedure

Setup:

  1. Place the tangent galvanometer on a leveled wooden platform
  2. Rotate the apparatus until the coil plane is in the magnetic meridian (North-South)
  3. Ensure compass needle is exactly at the center of the coil
  4. Check that needle moves freely without sticking
  5. Note the zero position (should point North when no current flows)

Measurement:

  1. Connect the coil in series with battery, rheostat, ammeter, and key
  2. Measure the radius of coil (r) and count number of turns (n)
  3. Close the key and adjust rheostat for a suitable current (start with ~0.5 A)
  4. Note the ammeter reading (current I)
  5. Observe compass needle deflection from North
  6. Read deflection angle θ from the scale (both sides for accuracy)
  7. Take average of left and right deflections
  8. Calculate: B = μ₀nI/(2r)
  9. Calculate: BH = B/tan(θ)
  10. Repeat with different current values (6-8 readings)
  11. Find mean BH

For Best Results:

💡 Real-World Applications

⚠️ Precautions

💬 Viva Questions & Answers

What is Earth's magnetic field?

Earth's magnetic field is the magnetic field that extends from Earth's interior into space, where it interacts with solar wind. Earth acts like a giant bar magnet with magnetic poles near the geographic poles. The field has horizontal component (BH), vertical component (BV), and total field BE = √(BH² + BV²).

State the tangent law.

Tangent law states: When a small magnetic needle is under the influence of two perpendicular uniform magnetic fields, the needle aligns itself in the direction of the resultant field, and tan(θ) = B/BH, where θ is the angle of deflection from the first field direction, B is the perpendicular field strength, and BH is the first field strength.

What is a tangent galvanometer?

A tangent galvanometer is an instrument used to measure electric current or Earth's horizontal magnetic field. It consists of a vertical circular coil and a compass needle at its center. When current flows through the coil, it creates a magnetic field perpendicular to Earth's field, causing the needle to deflect. The deflection angle follows the tangent law.

Derive the formula for BH using tangent galvanometer.

Magnetic field at center of coil: B = μ₀nI/(2r)
This field is perpendicular to Earth's BH.
By tangent law: tan(θ) = B/BH
Therefore: BH = B/tan(θ)
Substituting B: BH = μ₀nI/(2r tan(θ))
Where μ₀ = 4π×10⁻⁷ T·m/A, n = turns, I = current, r = radius, θ = deflection.

What is magnetic meridian?

Magnetic meridian is a vertical plane passing through the magnetic north and south poles. A freely suspended magnetic needle aligns itself in this plane. It's different from geographic meridian (which passes through geographic poles). The angle between them is called magnetic declination, which varies by location and time.

What is angle of dip?

Angle of dip (or magnetic inclination) δ is the angle that Earth's total magnetic field makes with the horizontal direction. It's measured using a dip circle. At magnetic equator, δ = 0° (field is horizontal). At magnetic poles, δ = 90° (field is vertical). Relationship: tan(δ) = BV/BH.

Why should the coil be in the magnetic meridian?

The coil must be in the magnetic meridian (North-South) so that the field produced by the coil is perpendicular to Earth's horizontal field. This perpendicular arrangement is essential for the tangent law to apply. If not aligned, the coil field won't be purely perpendicular to BH, causing error in deflection angle.

Why is deflection angle kept between 30° and 60°?

For maximum accuracy, deflection should be between 30° and 60° because: (1) tan(θ) changes most rapidly in this range, giving high sensitivity, (2) Near 0°, small errors in angle cause large errors in tan(θ), (3) Near 90°, tan(θ) → ∞, making calculations impractical, (4) Around 45° (tan 45° = 1), the setup is most sensitive to current changes.

What are the sources of error in this experiment?

Sources of error: (1) Coil not exactly in magnetic meridian, (2) Compass not at exact center of coil, (3) Nearby magnetic materials affecting field, (4) Non-uniform coil (not perfectly circular), (5) Parallax error in reading deflection, (6) Heating of coil changing resistance and current, (7) Earth's magnetic field fluctuations, (8) Inaccurate radius or turn count measurement.

Why do we reverse the current and take readings?

Reversing current reverses the direction of magnetic field produced by the coil, causing deflection in opposite direction. Taking average of both deflections eliminates: (1) Zero error of the scale, (2) Any systematic error in alignment, (3) Effect of nearby magnetic materials. This method is called "deflection method with reversal" and greatly improves accuracy.

What is the value of Earth's horizontal magnetic field?

Earth's horizontal component BH varies by location. Approximate values:
• At magnetic equator: maximum (~3.8 × 10⁻⁵ T)
• At magnetic poles: zero (field is purely vertical)
• In Nepal/India: ~3.2-3.8 × 10⁻⁵ T
• In temperate regions: ~2-4 × 10⁻⁵ T
The total field BE is about 5 × 10⁻⁵ T globally.

Can we use tangent galvanometer to measure current?

Yes! If Earth's horizontal field BH is known, the tangent galvanometer can measure current. From tan(θ) = B/BH and B = μ₀nI/(2r), we get: I = (2rBH tan(θ))/(μ₀n). However, it's not commonly used for current measurement because: (1) Low sensitivity for small currents, (2) Bulky size, (3) Affected by external fields, (4) Modern ammeters are more accurate and convenient.

What is the difference between BH and BE?

BH (horizontal component) is the component of Earth's field parallel to the surface, while BE (total field) is the actual magnitude of Earth's field including both horizontal and vertical components. Relationship: BE = √(BH² + BV²). At equator, BV = 0, so BE = BH. At poles, BH = 0, so BE = BV.

Why does Earth have a magnetic field?

Earth's magnetic field is generated by the dynamo effect in Earth's liquid outer core. The core contains molten iron and nickel. Earth's rotation causes this conducting fluid to move, creating electric currents. These currents generate magnetic fields, which in turn affect the fluid motion, sustaining the field. This is called the geodynamo process.

Do magnetic and geographic poles coincide?

No, they don't coincide. Magnetic poles are where Earth's magnetic field is vertical (dip = 90°), while geographic poles are at the ends of Earth's rotation axis. Currently, magnetic north pole is in northern Canada, about 500 km from geographic north pole. The angle between magnetic and geographic meridians is called declination, which varies by location. Also, magnetic poles slowly move over time.