Ferromagnetic Substances and Its Properties

Description:

The atoms of these materials like paramagnetic material have permanent magnetic dipole moments. The similar natures of dipoles are grouped in a small region called domain. These domains have a net magnetic moment in a particular direction. In the material, there are a large number of domains having magnetic moments in different directions making the net magnetic moment of the entire material zero. When the external magnetic field is applied to such ferromagnetic materials, then either the domains are oriented in such a way as to align with the direction of the field, or the size of the favorable domain increases. Generally, in the strong applied field the domains are aligned and in the weak field the size of the favorable domain increases. In both cases, the material is strongly magnetized in the direction of the applied external magnetic field.

Properties of Ferromagnetic Substances:

The properties of ferromagnetic substances are similar to the properties of diamagnetic substances but the difference is that diamagnetic substances are weakly magneties and ferromagnetic substances strongly magenties in the presence of magnetic field.

Properties of Ferromagnetism:

1.) If these materials are placed in an external magnetic field, they are strongly magnetized in the direction of the applied external magnetic field.

2.) Due to unpaired electrons, the atoms of ferromagnetic materials have a net magnetic dipole moment.

3.) Ferromagnetism arises due to the formation of domains.

4.) Magnetic susceptibility of these materials is high and positive and also inversely proportional to the absolute temperature:

$\chi=\frac{C}{T-T_{c}}$

where $T_{c}$ is Curie temperature.

5.) Relative permeability of these materials is much greater than 1.

6.) Magnetic moment is high but along the direction of the applied magnetic field.

7.) $Fe$, $Ni$, $Co$, etc. are examples of paramagnetic materials.

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High Monochromaticity of Laser Light

High Monochromaticity:

A laser beam is highly monochromatic. The monochromaticity of the laser beam is much more than that of any traditional monochromatic source. The line spread of a laser beam is very small in comparison to the light from a traditional source. This difference arises because conventional sources emit wave trains of very short duration and length, whereas, laser emit continuous waves of very long duration. The random spontaneous emission in the laser cavity is one of the mechanisms that determine a laser's ultimate spectral line width. It should be noted that no light source including laser light source, is perfectly monochromatic but a better approximation to the ideal condition may be considered in the case of the laser beam. The spread of light from a normal monochromatic source range over a wavelength of the order of $100 -1000 \overset{\circ}{A}$ while in lasers it is of the order of few angstroms $(\lt 10 \overset{\circ}{A})$ only.

The high spectral purity of laser radıation leads directly to applications in basic scientific research including photochemistry, luminescence excitation spectroscopy absorption, Raman spectroscopy, and also in communication. The degree of non-monochromaticity $\xi$ of light is characterized by the spread in frequency of a line by the line width $\Delta \nu $ and is expressed as:

$\xi=\frac{\Delta \nu}{ \nu_{\circ}}$

where $\nu_{\circ}$ is the central frequency. If $\Delta \nu $ approaches zero the degree of non-monochromaticity tends to zero which is an ideal condition. Absolute monochromaticity $(\Delta \nu =0)$ is not attainable in practice even with laser light. The spreads of two light sources, laser light, and normal light, are shown in the figure above. The degree of non-monochromaticity may also be written in terms of coherence time $(\tau_{C})$ or coherence length $(L_{C})$ as follows:

$\xi=\frac{1}{\tau_{C} \: \nu_{\circ}}$

$\xi=\frac{c}{L_{C} \: \nu_{\circ}}$

This relation shows that the monochromaticity will be large for higher values of coherence time or coherence length. The bandwidth of a laser light from a high-quality He-Ne gas laser is of the order of $500Hz$ $(\Delta \nu =500 Hz)$ corresponding to coherence length of the order of $600 km$ $(\tau_{C} = 2 \times l0^{-3} sec)$.

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Conversion of Galvanometer into a Voltmeter

What is a voltmeter?

A voltmeter is an instrument used to measure potential differences between two points in an electric circuit directly in volts. The instrument measuring the potential difference of the order of millivolt $(mV)$ is called a millivoltmeter. An ideal voltmeter has infinite resistance.

Galvanometer used as voltmeter:

To use the galvanometer as a voltmeter in the circuit, The resistance of the galvanometer should be very high or almost infinite as compared to the other resistance of the circuit. Because the internal resistance of an ideal voltmeter is infinity.

So a high resistance is connected in series with the galvanometer (pivoted-type moving-coil galvanometer).

When a high resistance is connected in series to the galvanometer then the resultant resistance increases as compared to the other resistance of the circuit and it can be easily used as an ammeter and the actual potential difference can be measured through it.

Mathematical Analysis:

Let us consider, $G$ is the resistance of the coil of the Galvanometer, and the $i_{g}$ current, passing through it, produces full-scale deflection. If $V$ is the maximum potential difference that exists between two points $a$ and $b$ in the circuit. On connecting the galvanometer across the points $a$ and $b$, a current $i_{g}$ passes through the galvanometer and a high resistance $R$ is connected in series with galvanometer then

$i_{g}= \frac{V}{G + R}$

$G + R= \frac{V}{i_{g}}$

$R= \left(\frac{V}{i_{g}}\right ) - G$

If the current $i_{g}$ in the coil produces a full-scale deflection, then for the potential difference $V$ between the points $a$ and $b$, there will be a full scale deflection. Thus, on connecting a resistance $R$ of the above valve in series with the galvanometer, the galvanometer will become a voltmeter of range $0$ to $V$ Volt.

Note:

For the voltmeter, a high resistance is connected in series with the galvanometer and so the resistance of a voltmeter is very high compared to that of a galvanometer.

Resistance of voltmeter

$R_{v}=R+G$

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Light Detection And Ranging (LIDAR)

LIDAR (Light Detection And Ranging):

The laser system used for monitoring the environment is known as LIDAR. LIDAR is an acronym that stands for "Light Detection And Ranging".

Before the discovery of the laser, the study of the atmosphere was carried out using an optical beam, the source being the search light. One such experiment was performed by Hulbert in 1937 to study the turbidity of the atmosphere. After the discovery of the laser as a source of an optical highly coherent beam, the study of the atmosphere was revolutionised.

A pulsed laser beam is transmitted into the atmosphere. It is scattered by the particles present in the atmosphere. The scattered radiations are picked up by a receiver. The receiver removes the background sunlight by using different filters. The scattered light gives information regarding the particles present in the atmosphere. Although microwaves can also give these characteristics, the results from laser beams are better in resolution and clarity. The different particles present in the atmosphere in colloidal form can be studied by a LIDAR. A schematic diagram of such a setup is shown in the Figure Below.

A photo detector is used to measure the time dependence of the intensity of the back-scattered laser beam. The time variation can be easily converted into the height (range) from which the laser beam has been back scattered the figure below shows a plot of time dependence of back scattered laser beam, which corresponds to height in the case of clear atmosphere with no aerosols, i.e., back scattering is by pure molecular gases such as $N_{2}$, $O_{2}$, $Ar$ etc. These molecules have dimensions much smaller than optical wavelength.

The scattering is of Rayleigh type. The figure below shows a plot of time dependence of backscattered light in the atmosphere contained aerosols (colloidal particles). These particles have dimensions comparable with the wavelength of laser light. This is Mie scattering. The curve in the figure below has kinks at points A and B between heights h and h. These kinks are due to the fact that between points $A$ and $B$, there are aerosols that are responsible for a greater intensity than that for a clear atmosphere. This implies the presence of aerosols between heights $h_{1}$ and $h_{2}$. With LIDAR, it is also possible to study the concentration and sizes of the aerosols present in the atmosphere. These are very important in atmospheric pollution studies.

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Comparison between electric charge and mass

Electric Charge:

1.) An electric charge can be positive, negative, or neutral.

2.) The electric charge of a body is always quantized and follows the equation: $q=ne$

3.) The electric charge of a body remains unaffected by its speed.

4.) Charge is strictly conserved.

5.) Electrostatic forces between two charged bodies can be either attractive or repulsive.

6.) Electrostatic forces between multiple charges can sometimes cancel each other out.

7.) A charged body always carries some mass.

Mass:

1.) The mass of a body is always positive.

2.) Unlike charge, mass quantization has not yet been established.

3.) The mass of a body increases with its speed.

4.) Mass is not conserved by itself as some of the mass may get changed into energy or vice versa.

5.) Gravitational forces between two masses are always attractive.

6.) Gravitational forces between multiple bodies never completely cancel out.

7.) A body with mass may not necessarily have a net charge.

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Weak nuclear force or interaction and its properties

What is weak nuclear force? 

Weak nuclear force is an act between only elementary particles involved in the nuclear process of $\beta$ - decay. The $\beta$ decay are two types

1.) Beta Pluse Decay
2.) Beta Minus Decay

1.) Beta Plus Decay:

When a beta plus decay occurs, a proton converts into a neutron and releases a positron $\&$ an electron-neutrino. It also reduces one atomic number of an element and converts it into another element.

2.) Beta Minus Decay:

When a beta minus decay occurs, a neutrons convert into a proton and releases an electron $\&$ electron-antineutrino. It also increases one atomic number of an element and converts it into another element.

In addition to beta decay, some scientists also find many other types of weak force like "charged-current" or "neutral-current". The charge is required for "charged-curent" but not for "neutral-current"; because of that, there are two types of charged carriers: one is the $W$ boson charge carrier and $Z$ boson.

Important properties of weak nuclear force :

1. Any process involving neutrino and antineutrino is governed by weak nuclear force because these particles can experience only weak interaction and not strong nuclear interaction.

2. The strength of weak nuclear force is greater than gravitational force and less than electromagnetic force.

3. It operates only in the range of nuclear size ($ \approx 10^{-15} m$).

4. The messenger particles that transmit the weak nuclear force between elementary particles are the massive vector bosons ($W^{\pm}, Z^{\circ}$).

5. The decay of in weak nuclear force (e.g., the decay of a pion to a muon and a neutrino) is much slower than the decay caused by strong nuclear or electromagnetic forces.

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Description of Errors in Measurement

Errors in Measurement

The following errors are likely to occur in the measurement of a physical quantity:

(1) Systematic Errors (arise due to known causes. The experimenter has control over the errors)
(2) Random Errors (arise due to unknown causes. The experimenter has no control over the errors)

(1) Systematic Errors:

When a measurement always has the same error (i.e. the nature or sign of the error is always of the same type, positive or negative), it is called systematic error.

Systematic errors occur due to known causes. These errors can be removed by knowing the causes.

Types of Systematic Errors:

(i) Constant Errors: If the measuring instrument is faulty from the point of view of its structure or design. That is, if the measurement marks made on the measuring instrument are wrong (faulty graduations), then by using such an instrument the error is always the same in all the observations. Such an error is called a constant error.

To remove static errors, an error-free measuring instrument should be used in place of the faulty measuring instrument and if this is not possible, then the nature of the error in the faulty instrument should be determined and measurements should be made as many times as possible.

(ii) Errors Due to Instruments: Such measuring instruments are error-free from the point of view of structure or design, but their excessive use causes defects in these instruments. Like zero error in vernier calipers or screw gauges, etc. Before starting the observation, such errors are found in all the measuring instruments used so that the final result of the measurement can be accurate.

(iii) Personal Errors: Those errors which arise due to the carelessness of the experimenter or the person doing the measurement are called personal errors. It does not depend on measuring instruments. This error can be reduced by increasing caution and taking readings correctly.

(iv) Errors caused by external factors (Errors due to External Reasons): Errors caused in observation due to changes in pressure, temperature, humidity, air velocity, etc. while taking observations are called errors caused by external factors.

These types of errors can be eliminated by adopting appropriate precautions and making possible arrangements to control environmental change. Can be done.

(2) Random Errors:

Such errors over which the experimenter has no control are called irregular errors. If the temperature, pressure, or humidity of the environment suddenly changes rapidly during observation or the supply voltage changes suddenly in any electrical experiment or the value of the earthquake exceeds the normal limit, then such changes have different effects in different experiments which affects the value of observation. These errors can be eliminated to a great extent by taking measurements several times and finding their average. Actual value can be found.

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