Category: Physics Notes PPT

Statistical physics is the plot of Physics. It has educated us with countless modules in the universe and will demonstrate us further. 

Statistical physics aims at learning the macroscopic factors of a system in equilibrium from the microscopic properties’ information through the law of mechanics. This method is not the same from thermodynamics that diagnoses the macroscopic system in equilibrium from the macroscopic position except seeing the microscopic parameters.

Statistical division is the division of statistical physics where a system is set up to determine free energy. In statistical physics, we practice the point that material contains atoms. On the basis of information of the microscopic laws that manage the atoms’ motion, and predominantly a surplus law of statistical physics. 

Thus, it provides an overall expression for the free (unrestricted) energy.

Statistical physics can help you to learn both thermal equilibrium states as well as non-equilibrium states.

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The above figure shows a molecular solid in which the individual particles are confined at specific lattice places and have no center of mass in motion.

Application of Statistical Physics

These are some statistical physics applications written below:

• The principal statistical physics application was focused on the dissemination of molecules in a gathering. It was functional in Maxwell’s distribution of molecular velocity.

• Gibb enlightened the thermodynamics in virtue of statistical physics.

Statistical Physics of Particles

Statistical physics has its beginnings in efforts to define the thermal properties of matter with regard to its fundamental particles and has performed an essential part in the advancement of quantum mechanics.

The statistical physics of particles is a specific explanation of numerous particles in statistical mechanics. 

A key requirement concept is that of a statistical ensemble (an idealism including the state space of probable states of a system, all categorized with a probability) that thoroughly highlights the properties of a large system at the cost of information about parameters of distinct particles.

When a group defines a system of particles with identical properties, their amount is named the particle number and is generally signified by N.

Statistical Physics of Fields

In abstract physics, statistical field theory, also known as SFT, is a theoretical outline that defines phase transitions. It does not mean a single theory but covers many models, such as magnetism, superfluidity, superconductivity, non-equilibrium phase transitions, wetting, and topological phase transition.

In statistical mechanics, SFT is denoted as an example where the degrees of freedom include fields or a field. Alternatively, the system’s microstates are stated through field formations.

These theories are broadly familiar for describing the systems in biophysics or polymer physics, such as polyelectrolytes, polymer films, or nanostructured block copolymers.

Elementary Statistical Physics

Statistical mechanics is one of the supporters of modern physics. It is identified by what means macroscopic observations (i.e., pressure and temperature) are linked to microscopic parameters that alter around an average. 

It connects thermodynamic quantities (for example, heat capacity) to microscopic actions, while, in standard thermodynamics, the only existing possibility would be measured and arranged such measures for numerous materials.

Statistical mechanics is essential for the ultimate learning of any physical system that possesses many degrees of freedom. The approach is based on statistical methods, probability theory, and microscopic physical laws.

It can be well known for explaining the thermodynamic performance of hefty systems. This division of statistical mechanics, which covers classical thermodynamics, is declared as equilibrium statistical mechanics or statistical thermodynamics.

It can also be used to learn systems that are beyond equilibrium. A significant sub-division branded as non-equilibrium statistical mechanics (occasionally titled as statistical dynamics) approaches the subject of microscopically modeling the speed of irretrievable processes that are motivated by inequalities. 

Illustrations of such procedures contain heat, or chemical reactions, or flows of particles.

Quantum Statistical Physics

Quantum statistical physics (denoted as quantum statistical mechanics in modern physics) is the statistical mechanics useful in quantum mechanical systems.

In quantum mechanics, a statistical ensemble (possibility circulation over potential quantum states) is defined by a density operator ‘S’, which is a self-adjoint, non-negative, trace-class machinist of trace 1 on the Hilbert space, ‘H’ recounting the quantum system.

This can be presented under numerous calculated properties for quantum mechanics. One such propriety is delivered by quantum logic.

Mathematical Statistical Physics

In mathematics, statistical physics is presented as statistical mechanics by J. Willard Gibbs in the year of 1902. 

This assemblage (also statistical group) is a magnification that includes a huge amount of virtual copies (occasionally extremely many) of a system, all measured simultaneously. Each of these signifies a probable state that the real system might have happened.

By another way of explanation, a statistical ensemble is a probability dispensation for the state of the system.

The precise diversity of ensemble among other assets, is in statistical equilibrium, and is used to determine the properties of thermodynamic systems from the laws of classical or quantum mechanics.

In the field of Electrostatics, which is a sub-concept of physics, we have a superposition principle. It is vital and plays a dominant role. So, let us try to understand the principle of superposition in detail. Like it’s a definition, extended topics of the superposition principle.

 

Define the Principle of Superposition

The principle of superposition definition helps us calculate the force uncharted, due to which the force can be caused by other charged particles that are acting on it. It also states that every charged particle creates some electric field, but the electric field is not dependent on any charged particles, whether they are present or absent. The principal also works on the combination of two or more electric fields. This electric field can be calculated by using the formula of Coulomb’s law. 

 

Principle of Superposition of Charges 

To explain the principle of superposition in electrostatics, it is better to perform an activity so that the principal can be understood and experienced through a practical.

Let us consider one positive energy, two negative energies. These may exert force on it, which creates electric charges. According to the principle of superposition,

The resultant force is the vector sum of all the forces acting on the body. This can be represented as,

[overrightarrow{F_{r}}]=[frac{1}{4pivarepsilon}][[frac{Qq_{1}}{r_{12}^{2}}widehat{r}_{12}+frac{Qq_{2}}{r_{13}^{2}}widehat{r}_{13}]]

Where,[widehat{r}_{12}] and [widehat{r}_{13}]are the unit vectors along the direction of q₁ and q₂.

∈ is the permittivity constant for the medium in which the charges are placed?

Q, q₁, and q₂ are the magnitudes of the charges respectively.

r₁₂and r₁₃  are the distances between the charges Q and q₁  &  Q and q₂ respectively. 

Using this formula for the superposition principle in electric field intensity, we can calculate the force of multiple charged particles. This is the Principle of Superposition. It can be seen in the following figure.

 

 

Continuous Charge Distribution

Along with the superposition principle in electrostatics, we need to get an idea about charge distribution. We know that we will get at least one charged atom, either positive or negative. This released the charged element is known as the proton. While the quantization of these protons, it is clear that the gap between them is very less and they are very closely bonded. So, here the charge distribution in them can be explained by stating the principle of superposition as follows in three ways. They are- 

• Linear charge distribution.

• Surface charge distribution.

• Volume charge distribution.

Linear charge distribution: The name itself specifies that the charge distribution will be in linear form. The charge is distributed uniformly to the entire path, whether it is a straight line or a circle. For circles, it is like the circumference of the circle. This linear charge distribution can be denoted byλ. Coulomb’s per meter is its measurement. it’s formula is, 

λ = dp/ dq .

Surface charge distribution:- If the charge can be distributed among the protons for a specific surface or a specific area of the hole, then it is called surface charge distribution. It is like a partial distribution. It can be measured as coulombs per square meter. It is denoted by σ. 

Volume charge distribution:- the third Way of quantizing charge distribution using the principle of superposition of electrostatic forces. Here the charge can be distributed throughout the volume of the surface. These are majorly observed in cylinders, Spears, etc., its measuring unit is columns per cubic meter. It is denoted by ρ.

If we observe one thing, the linear charge distribution is a straight line. So, the measuring unit is columns per meter. The next one is surface charge distribution, which applies to two-dimensional figures. So, it measures a unit of coulombs per square meter. Finally, the last one volume charge distribution can be used in three-dimensional figures like a sphere, cylinder, cone, etc. Hence the measuring unit is columns per cubic meter.

 

Linear Charge Distribution

The linear charge distribution is when charges are dispersed equally along a length, such as around the circumference of a circle or along a straight wire. The symbol for linear charge distribution is.

It is measured in Coulombs per meter and is [lambda =frac{text {dq}}{text{dl}}].

Surface Charge Distribution

Surface charge distribution: A surface charge distribution occurs when a charge is dispersed across a specified region, such as the surface of a disk, and is symbolized by the Greek letter σ.

The distribution of surface charges is determined. Cm^-2 is the unit of measurement or coulombs per square meter.

Volume Charge Distribution

When a charge is spread evenly throughout a volume, such as inside a sphere or a cylinder, it is said to be volume charge distribution. It is symbolized by the symbol.

The coulombs per cubic meter, or Cm^-3, is the unit of measurement for the volume charge distribution.

 

Conclusion

The principle of superposition in electrostatics for charges can be used to calculate the force applying to them. We also cover the charge distribution on those particles in three different ways. So, all the factors like wavelength, frequency, force, shape everything is countable and considerable.

The human eye is an essential organ, which interacts with light and is necessary for the sense of sight or vision. There are two kinds of cells in the eye i.e. rods and cones.

 

Conscious light perception, colour differentiation and perception of depth are done by these cells. The human eye can differentiate between about 10 million colors, and it can also detect a single photo. The human eye is a part of the sensory nervous system.

The eyes of all mammals have a non-image-forming photosensitive ganglion in the retina which receives light, adjusts the size of the pupil, regulates the supply of melatonin hormones, and also entertains the body clock.

We can be aware and see beautiful things around our environment, thanks to our vision. We learn 80% of what we know through our senses of sight. The way your eyes work is similar to how a camera does. They focus on the light that’s reflected in their eyes.

The cornea, iris, pupil, and lens make up the front of the eye, which focuses the image onto the retina. The light-sensitive membrane that covers the back of the eye is known as the retina. This membrane is made up of millions of nerve cells that clump together behind the eye to form the optic nerve, a huge nerve.

The Human Eye

The eye is one of the most significant and sophisticated sense organs that we have as humans. It aids in object visualization as well as the perception of light, colour, and depth. Furthermore, these sense organs are comparable to cameras in that they assist humans in seeing objects when light from the outside enters them. That so, learning about the structure and operation of the human eye is fascinating. It also assists us in comprehending the operation of a camera.

Six muscles are in the eye. They are responsible for controlling the movement of the eye. The most common kinds of muscles that are in the eye are the lateral rectus, medial rectus, inferior oblique, or superior rectus.

Parts of the Human Eye

• Pupil: The pupil is a small opening in the iris. The iris controls the size of the pupil. The pupil’s function is to adjust the amount of light entering the eye.

• Sclera: The outer covering of the eye is called the sclera. It is a protective tough white layer (white part of the eye).

• Cornea: The transparent part in front of the sclera is called the cornea. Light enters the eye through the cornea.

• Iris: It is a dark, muscular tissue and ring-like structure present behind the cornea. The colour of the eye is due to the colour of the iris. The iris regulates the amount and intensity of light entering the eyes by adjusting the size of the iris.

• Retina: It is the light-sensitive layer that consists of nerve cells. Its function is to convert the images formed by the lens into electrical impulses. These electrical impulses are then transmitted through optic nerves to the brain.

• Lens: The transparent portion situated behind the pupil is called the lens. The lens alters the shape to focus light on the retina, with the help of ciliary muscles. It becomes small to focus on objects at a distance and becomes big to focus on nearby objects.

• Optic Nerves:  You can find two types of optic nerves, which are cones and rods.

1. Cones: Cones are the nerve cells that are more sensitive to bright light. Cones help in central and colour vision.

2. Rods: Rods are the nerve cells that are more sensitive to dim lights. Rodes help in peripheral vision.

There are no sensory nerve cells at the junction of the optic nerve and retina. Therefore, no vision is possible at this point, and it’s called the blind spot.

Working of the Human Eye

The human eye operates similar to a digital camera in several ways:

• Light focuses mainly on the cornea, which acts like a camera lens.

• The iris controls the light that reaches the eye by adjusting the size of the pupil, and thus it functions like the diaphragm of a camera.

• The lens of the eye is located behind the pupil, and it focuses light. This lens helps the eye to automatically focus on near and distant objects, and also the approaching objects, like an autofocus camera lens.

• The cornea and lens focus light to reach the retina, which is a light-sensitive zone present on the inner lining of the back of the eye.

• The retina converts optical illusion images into electronic signals, and thus it acts as an electronic image sensor of a digital camera. These electric signals are then transmitted by the optic nerve to the visual cortex, which is responsible for the sense of sight.

The Function of the Human Eye

Human eyes are a specialized sense organ that is capable of receiving visual images, thereby producing the sense of sight in us. The eye receives direct oxygen through the aqueous humor. The aqueous humor nourishes the cornea, lens, and iris, by carrying nutrients, removing wastes materials excreted by the lens, and maintaining the shape of the eye. The aqueous humor is responsible for providing shape to the eye. It must be clear to function properly.

The Lens of the eye

The crystalline lens, also known as the lens of the eye, is a crucial component of the eye’s structure that allows the eye to concentrate on objects at various distances. It is situated in front of the vitreous body, behind the iris.

The lens seems to be an extended spherical — known as an ellipsoid — that resembles a deflated ball in its natural form. Adult lenses are roughly 10 mm across and 4 mm from front to rear in size.

Proteins make up virtually entirely of the lens. Proteins make up almost 60% of the lens of the eye, which is more than any other physiological tissue in terms of protein concentration. Because the tissue is translucent, light can easily enter the eye. It’s also bendable, allowing it to change shape and bend light to appropriately focus on the retina.

What is the Work of the Lens in the Human Eye?

The lens is a transparent flexible tissue located directly behind the iris and the pupil. The lens’ main job is to bend and concentrate light in order to create a sharp image. When concentrating on distant objects, the lens uses ciliary muscles to extend and thin out, and when focusing on close objects, the lens shrinks and thickens. The function of the lens is to focus light and images on the retina. The cornea and the lens are responsible for focusing the ima
ge in the retina.

Due to the elastic & flexible nature of the lens, it can change its curved shape to focus on nearby or distant objects depending on the need. The lens provides around 25-35 % of the total focusing power of the eye. The lens is attached to the ciliary muscles, which contracts and releases in order to change the shape of the lens and also its curvature.

The lens becomes oval-shaped to focus on near objects. The lens becomes elongated (or stretched) to focus on objects located at a far distance. When light enters the eye, the lens bends and focuses the light directly on the retina, producing the sharpest image possible.

On the retina, the crystalline lens projects a focused image. However, the projected image appears inverted at first (either upside down or reversed). The brain will flip the image back to normal when the image is given to it via the optic nerve.

The ciliary body is necessary for the lens to work properly. While the ciliary muscles allow the lens to change shape in order to focus, the lens is held in place by zonular fibres, or zonules, which are attached to the ciliary body. Aqueous humour is produced by the ciliary body, which keeps the lens healthy and functional.

Rather than nerves or blood flow, the lens gets its energy and is washed from the aqueous fluid. The aqueous humour is a transparent fluid that passes through the eye and subsequently drains through the trabecular meshwork.

 

Do You Know?

The human eye is blind for about 40 minutes every day. This is because of Saccadic masking; it is a way of the body to reduce motion blur while the object and eyes move. 20/20 is a normal vision and it’s not a perfect vision.

 

It means if a normal person can see an object at a distance of 20 feet, the test subject can also see the object at 20 feet. Hence the article covers all the necessary information related to the human eye. It discusses parts of the human eye and its function and working etc. It will be helpful for the students to understand the functioning of the human eye. 

We all have been there when we are not feeling like going to school due to the homework which we haven’t done. We try everything possible to make our parents believe that we have a fever and there is nothing we are going to miss today. Then our farther brings up the ultimate testing weapon, the thermometer, and all our dreams of having a rest day from school went up in smoke. Today we are going to talk about the technology behind thermometer and how one needs to read the thermometer correctly. 

What Is The Correct Reading Of The Thermometer?

Before we look at how to read a thermometer, lets first see how thermometer finds out the body temperature. On which mechanism does it work and what makes it provide us with accurate body temperature. In most of the cases, we see thermometer using Mercury as a liquid to measure the temperature. The thermometer is made from a glass tube that is sealed from both ends so that no fluid can escape it. When the temperature around the glass tube increases, the liquid starts to expand in the tube. As a result, we see the liquid go up and reach the higher units of temperature. 

The glass tube has a backboard inside in which the unit to measure temperature is marked. In everyday thermometer reading temperature, we have Fahrenheit unit of measurement. We measure the temperature by checking the level of the liquid on the backboard, which has degrees written on it. 

Furthermore, Alcohol is also used in lots of thermometers as it remains in liquid form in most of the temperature that we have on earth. It is easy to find an alcohol-based thermometer in school with the colour red or green to show us the temperature. On the other hand, Alcohol is not used when it comes to measuring high temperature as it starts to boils at 80 degrees Celsius. So in these cases, industries use Mercury as the base for thermometer liquid. 

Types of Thermometer

There are several ways to check the body temperature of an individual with the advancement in technology. Scientists and doctors have created a wide variety of thermometer which can be used to measure the body temperature. Given below is the list of different types of thermometer. 

Digital Thermometer 

This is not the latest thermometer that has been developed. But it is the most accurate one among all the temperature measuring thermometers out there in the market. Just like an old school thermometer you need to insert it in your mouth and put it under your tongue to measure the temperature.

Or you can put it under your arm to measure the temperature. You can find them in your local drug store, and they can be used both in the public and private environments. 

Forehead Thermometers

These are the latest thermometers that we see today, and they are pretty convenient as you don’t even have to get in contact with the patient. As a result, it is not as accurate as of the first one on our list. They read the heat signal using infrared technology. 

Plastic Strip Thermometers

If you want to know if the patient has a fever or not, you can use this thermometer. It’s more of the test then a thermometer, but still, a lot of doctors considered it to be one. You won’t be getting an exact temperature reading from this machine. It merely provides you with an indication of whether the person has a fever or not. To use it, all you need to do is put the strip on the forehead of the patient, and if the color changes to danger, the person might have a fever. 

Pacifier Thermometer

These are used in case of babies that are older than 3 months, and this thermometer requires a couple of minutes to provide you with an accurate reading.

Glass And Mercury Thermometer

Our last pick is glass and Mercury, this is the old combination, and it works like a charm, this thermometer configuration gives you the most accurate reading of the temperature. You need to place it inside your mouth, or you can put it in your armpit to measure the temperature.  

How To Measure Body Temperature By Thermometer?

Given below are the step that you need to follow to measure temperature from thermometer reading

1. First, wash your hands with soap and water. In addition to this, clean your thermometer sensor with rubbing alcohol and then rinse it.

2. Before taking the temperature, do not eat or drink for about 5 minutes at least. 

3. Now place the sensor of your thermometer under your tongue. 

4. Please keep it in the same position for roughly 50 seconds. 

5. If you have a digital thermometer, it will make a beeping noise once the reading is complete.

6. Otherwise, you can take it out after 50 seconds and note down the reading of liquid alongside the degrees.

The viscosity is a measure of the resistance of a fluid to flow. It defines the friction within a moving fluid. A fluid with large viscosity resists motion because it gives it a lot of internal friction due to its molecular structure. A fluid with low viscosity flows easily because when it is in motion, its molecular structure results in very little friction. For example, let’s take a funnel. Water flows very fast through a pipe, as it has very little flow resistance or very little viscosity. That is to say, it’s not very thick. On the other hand, it may take a little longer to run honey through a funnel. This is because it has greater flow resistance, more viscosity, and is thicker in nature.

What is the Coefficient of Viscosity?

The quantitative value of the viscosity i.e degree to which a fluid resists flowing under an applied force is called the coefficient of viscosity. There are two types of coefficient of viscosity.

Dynamic Viscosity: Dynamic viscosity(η) normally called viscosity is the ratio between the shearing stress (F/A) to the velocity gradient [(dv_{x}/dz)] in a fluid.

[eta = frac{frac{F}{A}}{frac{dv_{x}}{dz}}]

A common form of this equation is known as Newton’s equation which says the resulting shear of a fluid is directly proportional to the force applied and inversely proportional to its viscosity. 

[frac{F}{A} = eta left ( frac{dv_{x}}{dz} right ) Leftrightarrow F = frac{mdv}{dt}]

The SI unit of dynamic viscosity is pascal second and the common unit: dyne second per square centimeter([dyne – s/m^{2}]).

Kinematic viscosity: Kinematic viscosity(ν) is the ratio between the viscosity of a fluid to its density. Kinematic viscosity is a measure of a fluid’s resistive flux under gravity influence. 

[V = frac{eta }{rho}]

Units: SI unit: square meter per second ([m^{2}/s]). Common unit: square centimeter per second ([cm^{2}/s]).

Factors Affecting Viscosity

(Image to be added soon)

• Chemical Composition: The viscosity of liquids generally depends on their molecule’s size, shape, and chemical nature. It is greater with smaller molecules than with larger; with elongated molecules than with spherical ones. Normally large quantities of dissolved solids increase the viscosity.

• Colloid Systems: The lyophilic colloid solution has typically a fairly high viscosity

• Suspended Material: Suspended particles cause the viscosity to increase. 

Viscosity Experiment to Determine the Coefficient of Viscosity

Aim: 

Determine the viscosity coefficient of a given viscous liquid by measuring the terminal velocity of a given spherical organism (by Stokes method).

Material Required: 

A half-meter high transparent viscous liquid, one steel ball 5 cm broad glass cylindrical jar with millimeter graduations along with its height, screw gauge, clamp withstand, stop clock/watch, thermometer.

Theory

Terminal velocity: Terminal velocity is the maximum velocity attained by the object falling through a fluid. The acceleration of the object becomes zero when the summation of drag force and buoyancy equals the gravity, this makes the acceleration zero.

The formula for the terminal velocity: 

[V = frac{2r^{2}(rho – sigma )g}{9 eta} ]

Where,

v-terminal velocity

r-radius of the spherical body

g-acceleration due to gravity

ρ-density of the spherical body

σ-density of the liquid

η-coefficient of viscosity

Knowing ρ, σ, r, and calculating v, we can find the coefficient of the viscosity.  

Procedure:

• Clean the glass jar, and fill it with transparent viscous liquid.

• Verify that the vertical scale is clearly visible along with the height of the jar. Note its slightest count.

• Test the tight spring stopwatch. Find the least count and (if any) zero error.

• Find and note the screw gauge’s least count and zero error.

• Determine the mean ball radius.

• Drop the ball in the liquid, gently. It falls down with accelerated velocity in the liquid for about one-third of the liquid’s height. Then, uniform terminal velocity falls.

• When the ball hits a suitable division (20 cm; 25 cm; ……….) start the stopwatch. Note its downfall.

• Just when the ball hits the lowest convenient division (45 cm), stop the stopwatch.

• Find and note the falling distance and the time the ball has taken.

• Repeat steps 6 to 9 more than two times.

• Note, and record the liquid temperature.

• Record your remarks as given ahead here.

Observations:

• Least count of vertical scale = 1 mm

• Least count of stopwatch = …….. s

• Zero error of stopwatch = ……. s

• Pitch of screw gauge (p) = 1mm

• No.of divisions on the circular scale = 100

• Least count of the screw gauge (LC) = 1/100 = 0.01 mm

• Zero error of the screw gauge (e) = …… mm

• Zero correction of the screw gauge (c) =….. Mm

For the diameter of the spherical ball:

• Along one direction, [D_{1}] = ….. mm

• In the perpendicular direction, [D_{2}] = …….. Mm

For the terminal velocity of the spherical ball

Time took,

• [t_{1}] = …….. S

• [t_{2
  }] = …….. S

• [t_{3}] = …….. S

Result

The coefficient of viscosity of the liquid at a temperature (T℃) is ______

Note

• In gases, the viscosity coefficient increases with an increase in the temperature. 

• In the case of the liquid, the coefficient of viscosity decreases with an increase in the temperature. 

Types of Viscosity

Dynamic viscosity is defined as the tangential force per unit area necessary to move a fluid in one horizontal plane with respect to another plane at a velocity of unit value while the fluid’s molecules retain a unit distance apart.

Kinematic Viscosity

Kinematic viscosity is a type of viscosity calculated by dividing the fluid mass density by the dynamic fluid, viscosity, or absolute fluid viscosity. It’s also known as momentum diffusivity from time to time. Kinematic viscosity is measured in terms of time and fluid area. When no external force is applied except gravity, kinematic viscosity is the measurement of a fluid’s inherent resistance to flow. This is a force-independent quantity that is the ratio of dynamic viscosity to density. The kinematic viscosity of a fluid may be calculated by dividing its absolute viscosity by its mass density.

Application of Viscosity

The distinctive attribute of a liquid is viscosity, which is undifferentiated from the frictional force. The following are a few of the numerous applications of viscosity:

• High-thickness liquids are used in painting.

• Viscosity is considered while arranging food items such as dosas and chapatis.

• Pen ink is made up of liquids with a high viscosity.

• Paints, varnishes, and similar home items have their viscosity carefully controlled so that they may be applied easily and uniformly with a brush roller.

• Gum is made up of very sticky substances that cling to objects inexorably.

• The thickness of family unit items like paints and stains is directed in such a way that applying paint over the brush is straightforward.

• The viscosity of fluids affects blood circulation in arteries and veins.

• The oil drop experiment was used by Millikan to calculate the charge of an electron. He calculated the charge using his understanding of viscosity.

• Brake fluid transmits force via the braking system, and if it had a different viscosity, it would not function correctly.

When the current is passed through this loop, a magnetic field is produced which exerts a torque on the loops, rotating the shaft.

Here, the magnetic field is uniform all around it.

A current-carrying loop of wire in the above arrangement is attached to a vertical rotating shaft that feels magnetic forces that produce a clockwise torque as viewed from above.

This is how electrical energy is transformed into mechanical work.

Torque on a Current Loop in a Magnetic Field

If you look at Fig.1, four wires are joined to form a loop. They are placed inside the magnetic field.

When the current is passed through this loop, the magnetic field of lines crosses the loop. It experiences a force, which in turn generates a torque due to the force as shown in Fig.2.

Now, the loop will experience a force due to the magnetic field.

Here, the current is flowing from D to C and the magnetic field in the opposite direction.

To find the direction of the force in the wire CD.

Let’s Apply Fleming’s Right-Hand Rule

It states that if we stretch our index finger, middle finger and the thumb in such a way that they are mutually perpendicular to each other where the index finger indicates the direction of the magnetic field, middle finger, the direction of an induced current, while the thumb represents the direction of motion.

As we align our fingers in this way, we would observe that the current and the magnetic field are in opposite directions.

So, they are parallel, i.e. Sin 0° = 0.

Therefore, no force is acting on the wire CD. 

Similarly, if we look at wire AB, the direction of current is opposite to that in the wire CD, however in the same direction to that of the magnetic field.

Here also Sin 0° = 0, no force is acting on wire AB.

For wire CA,

The current is flowing in an upward direction, which means the electrons are flowing in the opposite direction. 

Applying Fleming’s right-hand rule, the magnetic field is in a direction perpendicular to that of current. The force is acting inwards.

While for the wire BD, the direction of the current is downward and the direction of force is outward.

A torque is exerted on the loop about an axis, making the loop rotate.

Now, we’ll deduce the equation for the same.

Torque on a Current Loop Equation

Here, we would define some quantities:

1. W  = width of the loop

2. L = Height of the loop, which is the length of the wire feeling the force.

3. F = IBL 

We took F = IBL because in maximum cases, F and B are perpendicular to each other and Sin 90° = 1.

So, an equation for torque:

て= Fd  (d = distance of the wire from the axis of rotation)

d  = W/2

As F = IBL

So,  てleft  (torque from the left) = (IBL) W/2 and てright = (IBL) W/2, and when the loop is in the middle, no torque will act on it.

てnet =   てleft  + 0 +  てright  = BIHW

∵  HW = A (area of the loop)

て = BIA

Here, area vector A points outward in the middle.

So, て = IABSinӨ     

   

If there are N number of loops inside the field, we have:

て = NIABSinӨ      …(1)

Torque on Current Loop due to the Magnetic Moment

From equation (1),

Here, NIA is called the magnetic moment.

So, torque on any current-carrying loop is the magnetic moment times the magnetic field.

Force is acting outwards whether the current is flowing inside or outside the loop, this magnetic force will continue spinning the loop.

Torque experienced by a Current Loop in a Uniform Magnetic Field

We know that the current loop when placed inside the magnetic field, behaves like a magnetic dipole where it has a North and the South pole.

So, magnetic moment, M = IA.

Now, consider a rectangular loop placed inside the magnetic field.

Explanation for Torque on Current Loop

Objects show certain movement or they exert a certain kind of force when pressure is used on them. For example, rotating a cap to open the bottle, removing the lid from a box, opening the door knob, tying the lace of the shoe and so on. These movements are torque movements which require some motion and are called rotational motions. Without the concept of a torque, there will be no movements at all. Torque is something that actually gives the rotational movement for all the objects without which we might not even be able to use these objects properly. 

The formula for torque is τ = F×r because torque is equal to the twisting force that tends to cause the movement or rotation. This formula is used when force (f) is applied to an object based on the distance ( r) between the center of rotation and to the point where force is applied. The direction of the torque can be found with the help of the right hand rule : where students have to curl their fingers on the right hand directed at the current and their thumb should stick out and point to the area vector. 

How to use Fleming’s Right Hand Thumb Rule 

To find out the direction of the torque, one can use the right hand thumb rule that was proposed by Fleming. By making sure that you are using the right formation, you can also find out the direction of the current. It is a common method to understand the directions and orientations of a three dimensional axis. We always have two possible orientations, so to see this:

This rule can also be used to find various other things like magnetic field, spirals, rotations, direction of the current and so on.