Tangent Galvanometer - Amrita University

Summary

This video script explains an experiment using a tangent galvanometer to determine the reduction factor and horizontal intensity of Earth's magnetic field. The apparatus includes a tangent galvanometer, commutator, rheostat, and other components. The principle is based on the tangent law, where the deflection of a needle in two perpendicular magnetic fields is used to calculate the horizontal magnetic field intensity. The procedure involves adjusting the galvanometer, applying a current, and measuring the deflection. The experiment can be repeated with different current values and coil turns for accuracy. The tangent galvanometer has applications in measuring small currents and determining Earth's magnetic field.

Takeaways

• 🧲 The tangent galvanometer (TG) is used to determine the reduction factor and the horizontal intensity of Earth's magnetic field.
• 🛠️ The setup includes a TG, commutator, rheostat, regulated DC power supply, ammeter, key, and connecting wires.
• 🌐 The TG consists of a coil wound on a non-magnetic frame which, when energized, produces a magnetic field perpendicular to Earth's magnetic field.
• 📐 The tangent law states that when a magnet is suspended in two magnetic fields, it rests at an angle where the magnetic field due to the current (B) is equal to the horizontal component of Earth's magnetic field (Bh) times the tangent of the angle (B = Bh * tan(theta)).
• 🔋 The magnetic field generated by the current-carrying coil at its center can be calculated using the formula B = (mu_0 * n * I) / (2 * a), where mu_0 is the permeability of free space, n is the number of turns, I is the current, and a is the radius of the coil.
• ⚖️ The reduction factor (K) of the TG is defined as the ratio of the magnetic field produced by the current in the coil to the deflection angle (K = B / tan(theta)).
• 📉 To measure the reduction factor and Earth's magnetic field intensity, the TG is adjusted to align with Earth's magnetic meridian, and the current is varied to achieve a deflection between 30 to 60 degrees.
• 🔄 The experiment involves reversing the current to ensure accurate readings and can be repeated with different current values and coil turns.
• 🔌 Proper connections are made with the power supply, rheostat, commutator, and TG to ensure the correct flow of current and measurement of deflection.
• 🌟 The tangent galvanometer has applications in measuring small currents and determining the horizontal intensity of Earth's magnetic field.

Q & A

What is the primary aim of using a tangent galvanometer?

The primary aim is to determine the reduction factor of the tangent galvanometer and the horizontal intensity of the earth's magnetic field.

What are the main components of the apparatus used in the experiment?

The main components include a tangent galvanometer, commutator, rheostat, regulated DC power supply, ammeter, key, and connecting wires.

How does the tangent galvanometer produce a magnetic field when current is passed through it?

The tangent galvanometer produces a magnetic field at the center of the coil, which is perpendicular to the earth's magnetic field, when current is passed through the circular coil of insulated copper wire.

What is the tangent law in magnetism as mentioned in the script?

The tangent law in magnetism states that when a bar magnet is suspended in two magnetic fields B and Bh, the magnet comes to rest making an angle (theta) with the direction of Bh, and the relationship is given by B = Bh * tan(theta).

How is the reduction factor of the tangent galvanometer defined?

The reduction factor of the tangent galvanometer (K) is defined as the ratio of the horizontal component of the earth's magnetic field (Bh) to the magnetic field generated by the current carrying circular coil (B).

What is the significance of the permeability of free space in the experiment?

The permeability of free space, denoted by μ₀ and equal to 4π × 10^-7 H/m, is used in the formula to calculate the magnetic field generated by the current carrying coil at the center.

What is the procedure for preliminary adjustments before starting the experiment?

The procedure includes adjusting the leveling screws to make the plane of the coil vertical, rotating the compass box so that its 90-90 line is in the plane of the coil, and rotating the tangent galvanometer to align the aluminum pointer with the 0-0 line in the compass box.

How is the current through the galvanometer adjusted for accurate results?

The current is adjusted using the rheostat until the galvanometer shows a deflection between 30 and 60 degrees for better and more accurate results.

What is the purpose of reversing the current using the commutator?

Reversing the current using the commutator allows for noting the corresponding deflection in the compass box, which is necessary for accurate measurements of the earth's magnetic field.

What are the applications of a tangent galvanometer as stated in the script?

A tangent galvanometer can be used for measuring small currents and for the determination of the horizontal intensity of the earth's magnetic field.

Outlines

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🧲 Tangent Galvanometer Experiment Overview

The paragraph introduces an experiment aimed at determining the reduction factor of a tangent galvanometer and the horizontal intensity of the Earth's magnetic field. The apparatus required includes a tangent galvanometer, a commutator, a rheostat, a regulated DC power supply, an ammeter, a key, and connecting wires. The tangent galvanometer operates on the principle of the tangent law, which states that when a bar magnet is suspended in two magnetic fields, it aligns itself at an angle with one of the fields. The experiment involves adjusting the galvanometer to align with the Earth's magnetic field and then using it to measure the magnetic field generated by a current-carrying coil. The reduction factor and the horizontal intensity of the Earth's magnetic field can be calculated using the tangent law and the properties of the coil.

Keywords

💡Tangent Galvanometer

A Tangent Galvanometer is an instrument used for measuring small electric currents. It operates on the principle of the tangent law in magnetism, where a current-carrying coil generates a magnetic field that interacts with the Earth's magnetic field, causing a deflection of a needle. In the script, the Tangent Galvanometer is used to determine the reduction factor and the horizontal intensity of Earth's magnetic field, illustrating its application in both scientific measurements and understanding the Earth's magnetic properties.

💡Reduction Factor

The reduction factor of a Tangent Galvanometer is a calibration constant that relates the deflection of the galvanometer's needle to the current passing through the coil. It is crucial for accurate measurements as it allows the conversion of the observed deflection into an actual current value. The script describes how this factor is determined by adjusting the current until a specific deflection is achieved, which is then used to calculate the Earth's magnetic field intensity.

💡Horizontal Intensity

Horizontal Intensity refers to the strength of the Earth's magnetic field in the horizontal plane. It is an important parameter in geomagnetism and is measured using devices like the Tangent Galvanometer. The script outlines a method to determine this intensity by setting up the galvanometer in the Earth's magnetic meridian and observing the needle's deflection when a known current is passed through the coil.

💡Commutator

A commutator is an electrical switch used to reverse the direction of an electric current in a circuit. In the context of the script, the commutator is used to reverse the current in the Tangent Galvanometer, which is necessary for accurate measurements as it allows for the observation of the needle's deflection in both directions, thus providing a means to check for any inconsistencies or errors in the setup.

💡Rheostat

A rheostat is a type of variable resistor used to control the amount of current flowing through a circuit. In the script, the rheostat is used to adjust the current in the Tangent Galvanometer, which is critical for achieving the desired deflection of the needle and, consequently, for obtaining accurate measurements of the Earth's magnetic field.

💡Regulated DC Power Supply

A regulated DC power supply provides a constant and stable direct current to a circuit. In the experiment described in the script, the power supply is used to provide a steady current to the Tangent Galvanometer, ensuring that the magnetic field generated by the coil is consistent and reliable for accurate measurements.

💡Ammeter

An ammeter is an instrument used to measure the current flowing through a circuit. In the script, the ammeter is connected to the Tangent Galvanometer to monitor the current being used, which is essential for adjusting the rheostat to achieve the desired needle deflection and for ensuring the accuracy of the measurements.

💡Tangent Law

The tangent law in magnetism states that when a magnet is suspended in two magnetic fields, it comes to rest at an angle where the tangent of the angle is proportional to the ratio of the magnetic fields. This law is fundamental to the operation of the Tangent Galvanometer, as it allows the relationship between the Earth's magnetic field and the field generated by the coil to be expressed mathematically, enabling the calculation of the reduction factor and the Earth's magnetic field intensity.

💡Deflection

Deflection in the context of the Tangent Galvanometer refers to the movement of the needle away from its equilibrium position due to the influence of magnetic fields. The script describes how the deflection of the needle is used to measure the Earth's magnetic field. The angle of deflection is crucial as it is directly related to the strength of the magnetic fields acting on the needle.

💡Magnetic Field

A magnetic field is a vector field that represents the magnetic influence on moving electric charges, electric currents, and magnetic materials. In the script, the magnetic field is central to the experiment as it describes how the Earth's magnetic field interacts with the magnetic field generated by the current in the Tangent Galvanometer's coil. Understanding the properties and behavior of magnetic fields is essential for interpreting the results of the experiment.

💡Permeability of Free Space

The permeability of free space, denoted by the Greek letter mu (μ), is a physical constant that relates magnetic field to magnetic flux density in a vacuum. It is a fundamental constant in electromagnetism and has a value of 4π × 10^-7 H/m. In the script, the permeability of free space is used in the formula to calculate the magnetic field generated by the current-carrying coil at the center, which is a critical step in determining the Earth's magnetic field intensity.

Highlights

Aim to determine the reduction factor of a tangent galvanometer and the horizontal intensity of earth's magnetic field.

Apparatus includes a tangent galvanometer, commutator, rheostat, regulated dc power supply, ammeter, key, and connecting wires.

Tangent galvanometer consists of a coil of insulated copper wire wound on a non-magnetic frame.

Deflection of the needle occurs due to the interaction of the magnetic field produced by the coil and earth's magnetic field.

The tangent law is the working principle behind the tangent galvanometer.

The tangent law states that B = Bh * tan(theta), where B is the magnetic field produced by the coil and Bh is the horizontal component of earth's magnetic field.

The reduction factor of the tangent galvanometer (K) is defined and can be calculated using the formula K = (Bh / B) * tan(theta).

The horizontal intensity of earth's magnetic field (Bh) can be determined using the tangent galvanometer.

Procedure involves preliminary adjustments to ensure the coil's plane is vertical and aligned with earth's magnetic meridian.

The experiment requires connecting the power supply, ammeter, rheostat, and tangent galvanometer in a specific configuration.

The current through the galvanometer is adjusted for a deflection between 30 and 60 degrees for accurate results.

The experiment is repeated with different current values and varying the number of turns in the galvanometer for reliability.

Tangent galvanometer can measure small currents and is used for determining the horizontal intensity of earth's magnetic field.

The experiment involves reversing the current to ensure accurate readings and account for any bias.

The tangent galvanometer's reduction factor is crucial for accurate measurements of earth's magnetic field.

The tangent galvanometer's application extends to the study of small currents and magnetic field measurements.

The experiment setup includes a detailed connection diagram for ease of understanding and replication.

The tangent galvanometer's operation is based on the interaction of magnetic fields, which is a fundamental principle in magnetism.

Transcripts

Tangent Galvanometer

Aim:

To determine the reduction factor of a tangent galvanometer and the horizontal intensity

of earth's magnetic field using a tangent galvanometer.

Apparatus:

Tangent galvanometer (TG), commutator (C), rheostat (Rh), regulated dc power supply (E),

ammeter (A), key (K) and connecting wires.

Tangent galvanometer consists of a coil of insulated copper wire wound on a circular

non- magnetic frame. When a current is passed through the circular coil, a magnetic field

is produced at the center of the coil, which is perpendicular to rarth's magnetic field.

Since the needle is under the action of these two perpendicular magnetic fields, it is deflected

from the mean position.

Principle:

The working principle behind th tangent galvanometer is the tangent law.

When a bar magnet is suspended in two magnetic fields B and Bh, the magnet comes to rest,

making an angle (theta) with the direction of Bh as shown in the figure.

That is B=Bh tan (theta)

This is called the tangent law in magnetism.

Theory:

Usually TG is arranged in such a way that the horizontal component of earth's magnetic

field is in the direction of the plane of the coil. When a current flows through the

circular coil, the magnetic needle is under the action of two mutually perpendicular fields.

If theta is the deflection of the needle, then according to tangent law:

Where Bh is the horizontal intensity of earth's magnetic field and B is the field generated

by the current carrying circular coil.

If 'I' is the current passing through the coil of radius 'a' with 'n ' number

of turns, then the field generated by the coil at the center is:

Where is the permeability of free space, which is equal to 4pi 10-7 Hm-1 (Henry meter raise

to -1).

Equating (1) and (2), we get:

The reduction factor of tangent galvanometer K can be defined as:

From the above expression, the horizontal intensity of earth's magnetic field Bh can

be written as:

Procedure:

Preliminary adjustments:

Adjust the leveling screws, to make the plane of the coil vertical.

The compass box alone is rotated so that its 90-90 line is in the plane of the coil.

The tangent galvanometer, as a whole, is rotated so that the aluminium pointer reads 0-0 line

in the compass box. Now the tangent galvanometer is in the magnetic

meridian of earth.

Determination of reduction factor and horizontal intensity of earth's magnetic field.

The positive terminal of the power supply is connected to the positive end of ammeter

via the key and then to the one end of rheostat. The negative terminal of the supply and the

top end of the rheostat are connected at 1 & 3terminals of the commutator. The two ends

of the tangent galvanometer are connected at 2 & 4 terminals of the commutator.

Now the entire connection will be as shown in figure.

Where K is the key, E battery, A ammeter, Rh rheostat, C commutator, and TG the tangent

galvanometer.

Select the number of turns in the coil (say 5).

Allow a suitable current in the circuit by adjusting the rheostat and inserting the key

K. For better and more accurate results, the

current through the galvanometer is adjusted until the galvanometer shows deflection in

between 30 and 60 degrees. The corresponding deflection in the compass

box is noted. Reverse the current using the commutator and

again note the readings.

The entire experiment can be repeated for different values of current and by changing

the number of turns in the tangent galvanometer.

Applications:

Tangent galvanometer can be used for measuring small currents.

It is used for the determination of horizontal intensity of earth's magnetic field.