Stewart and Gee’s Experiment Viva Questions | apniPhysics

Last updated on Wednesday, May 22nd, 2024

Stewart and Gee’s Method

Determination of Magnetic Field along the Axis of a Current-Carrying Circular Coil

1Q. What is the magnetic induction formula at a point x, away from the center of the circular coil?

The magnetic induction formula at a point x, away from the center of a circular coil carrying a current I can be given by the Biot-Savart law, which states that:

B = (μ₀I/4π) ∫dl × r / r³

where:

B  is the magnetic field induction at the point x,
μ₀ is the permeability of free space,
I  is the current flowing through the circular coil,
dl is an infinitesimal element of the circular coil,
r  is the position vector from the element dl to the point x, and
×  denotes the vector cross product.

To calculate the magnetic field induction at the point x, we need to integrate the above expression over the entire circular coil. The direction of the magnetic field is perpendicular to the plane of the circular coil and follows the right-hand rule, which can be determined by curling the fingers of the right hand in the direction of the current and the thumb will point in the direction of the magnetic field.

2Q. What will be the Magnetic field value at the center of a current-carrying coil?

The magnetic field at the center of a current-carrying coil can be calculated using the Biot-Savart law, which relates the magnetic field at a point to the current flowing through a wire or a coil. For a circular coil carrying a current I, the magnetic field at its center can be calculated as:

B = (μ₀IN)/2*R

where μ₀ is the permeability of free space, I is the current in the coil, N is the number of turns in the coil, and R is the radius of the coil.

From this equation, we can see that the magnetic field at the center of a current-carrying coil is directly proportional to the current in the coil, the number of turns in the coil, and the radius of the coil. Therefore, if we increase the current, the number of turns or the radius of the coil, the magnetic field at the center will also increase.

For example, if we have a circular coil with a radius of 0.1 meters, carrying a current of 2 amperes and with 100 turns, the magnetic field at its center can be calculated as:

B = (4π×10^-7 * 2 * 100) / (2 * 0.1) ≈ 1.26 x 10^-3 Tesla

So, the magnetic field at the center of this coil is approximately 1.26 milli-Tesla.

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3Q. Does earth’s horizontal magnetic field value remain the same everywhere or it fluctuates?

The horizontal component of Earth’s magnetic field, also known as the magnetic declination or magnetic variation, is not constant and varies in both time and location. It is influenced by many factors, including the position of the observer on Earth, the movement of conducting fluids in Earth’s core, and the interaction of the magnetic field with the solar wind and other space weather phenomena.

The horizontal magnetic field can vary significantly over short distances, particularly near the magnetic poles, where it can change rapidly as a result of the complex behavior of the Earth’s magnetic field. In addition, the magnetic declination also changes over time, as the position of Earth’s magnetic north pole drifts slowly over the surface of the Earth due to changes in the Earth’s magnetic field.

To account for the variation in Earth’s magnetic field, magnetic declination charts are published by various organizations, which provide information about the magnetic declination at different locations around the world, and how it changes over time. These charts are used by navigators, surveyors, and other professionals who need to take the magnetic field into account in their work.

4Q.What are the two factors to calculate the earth’s horizontal magnetic field value online (https://www.ngdc.noaa.gov/geomag-web/#igrfwmm)

The angle measured by a Deflection Magnetometer is usually in reference to the Earth’s magnetic field component. The purpose of the Deflection Magnetometer is to measure the angle between the Earth’s magnetic field and the magnetic field of a current-carrying coil or a bar magnet. This angle is known as the magnetic declination or magnetic variation.

By measuring the magnetic declination, one can determine the direction of the Earth’s magnetic field at a particular location. This information can be useful in many applications, such as navigation, surveying, and geophysics.

However, it is worth noting that the angle measured by the Deflection Magnetometer can also be affected by the magnetic field produced by the current-carrying coil or the bar magnet being measured. This is because the magnetic field produced by the coil or magnet can interact with the Earth’s magnetic field and cause a deviation in the angle measured by the instrument. Therefore, in order to obtain an accurate measurement of the magnetic declination, it is important to ensure that the magnetic field produced by the coil or magnet is sufficiently weak compared to the Earth’s magnetic field.

6Q. Why do you put apparatus (Wooden Frame along with circular coil) in East-West Direction?

A wooden frame apparatus is used in conjunction with a circular coil to create a Deflection Magnetometer, which is an instrument used to measure the magnetic field at a particular location.

The circular coil is mounted on the wooden frame so that it can rotate about a horizontal axis. When the coil is aligned in the East-West direction, it is perpendicular to the Earth’s magnetic field lines, which are also roughly aligned in the East-West direction at most locations on the Earth’s surface. This alignment allows the coil to detect any deviation or deflection in the Earth’s magnetic field caused by the presence of nearby magnetic materials or currents.

The wooden frame is used to minimize the effect of external magnetic fields on the coil. Wood is non-magnetic, so it does not interfere with the magnetic field measurements. By mounting the coil on the wooden frame, it is isolated from any external magnetic fields that might be present in the laboratory or the surrounding environment.

In summary, the wooden frame apparatus is used in conjunction with a circular coil in the East-West direction to minimize the effect of external magnetic fields and to allow the coil to detect any deviation or deflection in the Earth’s magnetic field caused by the presence of nearby magnetic materials or currents.

7Q. What is commutator and what its role in an experiment?

In the context of an experiment involving a current-carrying coil, a commutator may be used to reverse the direction of the current in the coil. This can be useful for studying the effects of the magnetic field produced by the coil on nearby objects or for investigating the behavior of the coil itself.

For example, if a circular coil of wire is used to produce a magnetic field, the direction of the magnetic field will depend on the direction of the current flowing through the coil. By using a commutator to reverse the direction of the current, the direction of the magnetic field can be changed, allowing the experimenter to study the effects of the magnetic field in different directions.

In addition, a commutator may also be used in conjunction with a DC power source to produce a rotating magnetic field. By using multiple coils and a commutator to switch the direction of the current, a rotating magnetic field can be created, which is the basis for many types of electric motors and generators.

In summary, a commutator is a device used to reverse the direction of the current in an electric motor or generator, and in the context of an experiment involving a current-carrying coil, it can be used to change the direction of the magnetic field produced by the coil, or to create a rotating magnetic field.

8Q. What is the difference between the Helmholtz coil and Solenoidal?

Helmholtz coils and solenoidal coils are both types of coils used to generate a magnetic field, but they differ in their shape, arrangement, and the type of magnetic field they produce.

Helmholtz coils consist of two identical coils of wire with equal radii, placed parallel to each other and separated by a distance equal to their radius. The coils are connected in series and carry equal and opposite currents. The magnetic field produced by a Helmholtz coil is uniform and parallel to the axis of the coils, with the field strength varying only slightly over the region between the coils. Helmholtz coils are often used in experiments where a uniform magnetic field is required, such as in studies of magnetism, electromagnetism, and optics.

Solenoidal coils, on the other hand, consist of a single coil of wire wound in a cylindrical shape with a uniform spacing between the turns. The magnetic field produced by a solenoidal coil is not uniform, but it has a strong axial component and a much weaker radial component. Solenoidal coils are often used in experiments where a strong magnetic field is required, such as in studies of high-energy physics, nuclear magnetic resonance (NMR), and magnetic resonance imaging (MRI).

In summary, the main differences between Helmholtz coils and solenoidal coils are their shape, arrangement, and the type of magnetic field they produce. Helmholtz coils produce a uniform magnetic field parallel to the axis of the coils, while solenoidal coils produce a non-uniform magnetic field with a strong axial component and a weak radial component.

READ ALSO: Melde’s Experiment

9Q. What is the relation between Gauss and Tesla?

Gauss and Tesla are both units of magnetic field strength, but they are defined in different systems of units.

Gauss (G) is a unit of magnetic field strength in the CGS (centimeter-gram-second) system of units. One gauss is equal to one maxwell per square centimeter, where a maxwell is the unit of magnetic flux. In SI units, one gauss is equal to 0.0001 tesla.

Tesla (T) is the unit of magnetic field strength in the SI (International System of Units) system. One tesla is equal to one weber per square meter, where a weber is the unit of magnetic flux. In CGS units, one tesla is equal to 10^4 gauss.

Therefore, one tesla is equal to 10,000 gauss, and one gauss is equal to 0.0001 tesla. The relationship between gauss and tesla can be expressed as:

1 T = 10,000 G
1 G = 0.0001 T

In summary, gauss and tesla are units of magnetic field strength used in different systems of units, and one tesla is equal to 10,000 gauss.

10Q. What is the unit of magnetic field intensity H?

The unit of magnetic field intensity H is ampere-turns per meter (A-turn/m or A/m). This unit is used in the International System of Units (SI) to measure the strength of a magnetic field produced by a current-carrying coil or a magnetizing field.

The unit of A-turn/m indicates the amount of current flowing through a coil of wire, which is measured in amperes, and the number of turns of wire in the coil. The magnetic field intensity H is related to the magnetic field strength B by the equation:

B = μH

where μ is the permeability of the material, which relates the magnetic field to the magnetic flux density.

In summary, the unit of magnetic field intensity H is A-turns per meter (A-turn/m or A/m) and is used to measure the strength of a magnetic field produced by a current-carrying coil or a magnetizing field.

11Q. When you plot the graph in-between the tan-theta and distance, you observe Gaussian type shape of the curve. On this curve, you find the points of inflection what is the formula for that?

When plotting the graph of tan-theta vs. distance for a deflection magnetometer experiment, one may observe a Gaussian-type shape of the curve, with a peak at the center and symmetric tails on either side. The points of inflection on this curve can be used to determine the horizontal component of the earth’s magnetic field, and they can be found using the formula:

d = √[(2n-1)R²/(2n+1)]

where d is the distance from the center of the coil to the point of inflection, R is the radius of the coil, and n is an integer representing the order of the point of inflection. The first order point of inflection corresponds to n=1, the second order to n=2, and so on.

The formula can be derived using the properties of the Gaussian distribution, which has a bell-shaped curve with a standard deviation proportional to the width of the curve. The distance between two adjacent points of inflection is given by:

Δd = √[(2n+1)R²/(2n+3)] – √[(2n-1)R²/(2n+1)]

which can be simplified to:

Δd ≈ R/√(n)

This shows that the distance between adjacent points of inflection decreases as the order of the point of inflection increases, and it also depends on the radius of the coil. The points of inflection can be used to determine the horizontal component of the earth’s magnetic field by measuring the distance between adjacent points and using the formula:

B_h = 2πI/(μ₀nΔd)

where B_h is the horizontal component of the magnetic field, I is the current in the coil, μ₀ is the permeability of free space, n is the order of the point of inflection, and Δd is the distance between adjacent points of inflection.

12Q. The magnetic field of induction increases one side of the center and decreases on other sides. Can we create a uniform magnetic field with the help of this concept?

Yes, it is possible to create a uniform magnetic field using the concept of the magnetic field of induction increasing on one side of the center and decreasing on the other sides.

One way to create a uniform magnetic field is by using a pair of identical coils that are separated by a distance equal to their radius. These coils are often referred to as Helmholtz coils, and they are wired in series so that the current flows in the same direction through both coils. The magnetic field created by each coil adds together to produce a uniform magnetic field along the axis that passes through the center of the coils.

The magnetic field produced by a single coil decreases as the distance from the center of the coil increases, resulting in a non-uniform magnetic field. However, when two coils are used in this configuration, the magnetic field produced by one coil is canceled out by the magnetic field produced by the other coil, resulting in a uniform magnetic field along the axis between the coils.

By adjusting the radius of the coils and the distance between them, it is possible to create a uniform magnetic field with a desired strength and direction. This type of setup is commonly used in scientific experiments and industrial applications that require a uniform magnetic field, such as in magnetic resonance imaging (MRI) machines or in particle accelerators.

13Q. How many turns (50, 100, 500, 1000, etc)  you have used in your experiments in the current-carrying coil?

The number of turns that can be used in an experiment with a current-carrying coil depends on the specific application and the desired strength and configuration of the magnetic field.

In general, increasing the number of turns in a coil increases the strength of the magnetic field it produces, but also increases the resistance and inductance of the coil, which can affect the performance of the experiment.

For many applications, a few hundred turns may be sufficient to produce the desired magnetic field, but for more specialized applications such as in particle accelerators, thousands or even millions of turns may be necessary.

Ultimately, the optimal number of turns will depend on a number of factors, including the specific application, the properties of the materials being used, and the available power supply and instrumentation. It is often necessary to experiment with different numbers of turns to find the best configuration for a particular experiment.

14Q. Can you perform the experiment by using the Alternating Current?

Yes, it is possible to perform an experiment using alternating current (AC) with a current-carrying coil. However, there are a few key differences between using AC and direct current (DC) in this type of experiment.

When using DC, the magnetic field produced by the coil is constant over time, while with AC, the magnetic field changes direction and magnitude with the frequency of the current. This means that the measurement and interpretation of the magnetic field may be more complex when using AC, as the field will be oscillating and changing direction at a given frequency.

Additionally, when using AC, the impedance of the coil and its surrounding circuitry may become a factor. This is because the impedance of the coil will vary with the frequency of the AC, which can affect the performance and accuracy of the measurement. Specialized equipment may be necessary to ensure that the AC is at the correct frequency and that the measurement is accurate and meaningful.

In summary, it is possible to perform experiments with a current-carrying coil using AC, but it may require specialized equipment and techniques to accurately measure and interpret the magnetic field produced by the coil.

15Q. Do you feel any application of this experiment?

Yes, there are many applications of the experiment involving current-carrying coils and magnetic fields, both in scientific research and in industry.

Some examples of applications include:

Magnetic levitation and transportation: By using the magnetic force produced by current-carrying coils, it is possible to create levitating objects or to move objects along a track without physical contact. This technology is used in high-speed trains, magnetic bearings, and maglev transportation systems.

Medical imaging: Magnetic resonance imaging (MRI) machines use strong magnetic fields produced by current-carrying coils to create detailed images of the inside of the body. This technology is widely used in medical diagnosis and research.

Electromagnetic induction: The principle of electromagnetic induction is used in many devices, including transformers, generators, and motors. These devices use the magnetic field produced by current-carrying coils to convert electrical energy into mechanical energy, or vice versa.

Scientific research: Magnetic fields produced by current-carrying coils are used in a wide range of scientific research, including in the study of fundamental particles and the behavior of materials in extreme environments.

Overall, the experiment involving current-carrying coils and magnetic fields has many practical and scientific applications, and has contributed to significant advances in technology and knowledge.

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For any updates please feel free to ask questions, or comment in the box.

Frequently Asked Questions

Question: What is the use of a commutator?
Answer: Reverse the Direction of Current: The commutator helps reverse the direction of the electric current in the coils of wire that make up the armature (rotating part) of the motor or generator. This reversal of current direction is essential for the continuous rotation of the motor or the generation of alternating current (AC) in a generator.

Question: What is the value of Earth magnetic field?
On average, the strength of the Earth’s magnetic field at the surface is approximately 25 to 65 microteslas (µT), which is equivalent to 0.25 to 0.65 gauss.

Question: What is the unit of magnetic field?
Answer: The unit of magnetic field strength is the tesla (T), named after the Serbian-American inventor and engineer Nikola Tesla. One tesla is defined as one newton per ampere-meter (N/A·m), which can be further expressed as:

1 T = 1 N/(A·m)

In smaller units, the millitesla (mT) and microtesla (µT) are commonly used:

1 millitesla (mT) = 0.001 tesla (T)
1 microtesla (µT) = 0.000001 tesla (T)
These units are used to measure the strength of magnetic fields in various contexts, including physics, engineering, geophysics, and environmental sciences.

Question: What is the SI unit of Earth magnetic field?
The SI (International System of Units) unit for measuring the strength of Earth’s magnetic field is the tesla (T)