Basic Science Knowledge

Keplers’s Laws of Planetary Motion, Kepler's Law, Law of Orbits, Law of Areas, Law of periods

noreply@blogger.com (Knowledge world) — Sun, 17 Jul 2022 10:56:00 +0530

Keplers’s Laws of Planetary Motion:

1^stlaw ( Law of Orbits ):

Every planet moves around the sun in elliptical orbit with the sun at one of the foci of the elliptical orbit.

2^ndlaw ( Law of Areas):

The line joining the planet to the sun sweeps over equal areas in equal intervals of time.

Area of SAB = Area of SCD

2^ndlaw tells us that a planet does not move with constant speed around the sun. It speeds up while approaching the nearest point called ‘ perigee’ and slows downs while approaching the farthest point called ‘ apogee’. therefore, distance covered on the orbit with in the given interval of time at perigee is greater than that at apogee such that areas swept are equal.

3^rdLaw ( Law of periods):

The square of the time periods of revolution of a planet around the sun is directly proportional to the cube of the mean distance of a planet form the sun.

The law is mathematically expressed as

Thought kepler gave the laws of planetary motion, he could not give a theory to explain the motion of planets.

Only Newton explained that the cause of the motion of the planets is the gravitational force which the sun experts on them.

Newton used kepler’s 3^rd law to develop the law of universal gravitation.

Gravitational Forces of the earth or Gravity, The gravitational force of the earth (or gravity) is responsible, A few facts about Lunar Tides, Newtons’s Universal Law of Gravitation, Properties of gravitational forces, Universal Gravitational Constant (G),

noreply@blogger.com (Knowledge world) — Sat, 16 Jul 2022 13:56:00 +0530

Gravitational Forces of the earth or Gravity

A force is necessary to produce motion in a body.

A body dropped from a height falls toward the earth. It indicates that the earth exerts a force of attraction (called gravity) on the body.

In fact, the earth attracts all the object its centre.

The force with which the earth pulls the object toward it is called the gravitational force of the earth or gravity.

The gravitational force between the sun and the earth keeps the earth in uniform circular motion around the sun.

The gravitational force of the earth (or gravity) is responsible -

l For holding the atmosphere above the earth.

l For the rain falling to the earth.

l For flow of water in the rivers.

l For keeping us firmly on the earth.

l For the revolution of moon around the earth, etc.

The gravitational force between the earth and the moon causes tides in the sea. Think why tides are high during full moon and new moon day.

A few facts about Lunar Tides.

The gravitational force of the moon in one ten- million that of earth, but when you combine other force such as the earth’s centrifugal force created by its spin, you get tides.

The sun’s gravitational force on the earth is only 46% that of the moon, making the moon the single most important factor foe the creation of tides.

The sun’s gravity also produces. Tides but since the forces are similar, as compared to the moon, the effects are greatly decreased.

Tides are not caused by the direct pull of the moon’s gravity. The moon is pulling upward on the water while the earth is pulling downward. Slight advantage to the moon and thus we have tides.

Whenever the moon, earth and sun are aligned the gravitational pull of the sun adds to that of the moon and thus moon causing maximum tides.

Spring tides happen when the sun and moon are on the same side of the earth ( New Moon) or when the sun and moon are on opposite sides of the earth ( Full Moon)

When the moon is at first quarter or last quarter phase (meaning that it is located at right angles to the Earth-sun line ), the sun and moon interface with each other in producing tides bulges and tides are generally weaker’; these are called neap tides.

Offshore, in the deep ocean, the difference in tides is usually less than 1.6ft.

The surf grows when it approaches a beach, and the tides increases. In bays and estuaries, this effect is amplified. ( in the Bay of Fundy, tides have a range of 44.6ft.)

The highest tides in the world are the Bay of Fundy in Nova Scotia, Canada.

Because the earth rotates on its axis the moon complete one orbit in our sky every 25hours (Not to be confused with moon’s 27 day orbit around the earth), we get two tidal peaks as well as two tidal troughs. These events are separated by about 12 hours.

Since the moon moves around the earth it is not always in the same place at the same time each day. So, each day, the times for high and low tides change by 50 minutes.

The type of gravitational force that causes tides is known as Tractive force.

Newtons’s Universal Law of Gravitation

Every body in the universe attracts every other body with a force which is directly proportional to the product of their masses and is inversely proportional to the square of the distance between them.

The direction of force is along the line joining the center of the two bodies.

Let two bodies A and B of masses m₁and m₂ are placed at a distance of “r” from each other. Let “f” be the force of attraction between the bodies.

Then,

The force of attraction is directly proportional the product of their masses

F α m₁m₂

The force of attraction is inversely proportional the square of the distance between them

Where G is a constant called as “ universal gravitational constant.

Properties of gravitational forces

1. Gravitational forces is the weakest force in nature

2. It is an attractive force. ( unlike electrostatic and magnetic forces; they are both attractive and repulsive )

3. It is a mutual force. ( first body attracts the second body and the second body attracts the first body with equal forces)

4. It is a centre force ( acts along the line joining the centers of the bodies)

5. It is a mass and distance dependent.

6. It obeys inverse square law.

7. It is a long range force ( it decreases with distance as per inverse square law and become zero only at infinite distance - like electrostatics and magnetic forces)

8. It does not depends on the medium between the interacting bodies. ( their is no gravitational shielding)

Universal Gravitational Constant (G):

G = F r²/ m_2*m₂

The value of Universal Gravitational constant G is 6.67*10^-11Nm²kg^-2

The value of G does not depends on the medium between two bodies.

The value of G is same throughout the universe and hence the name.

Universal Gravitational Constant G is different from acceleration due to gravity g. Therefore correct symbol must be used accordingly.

S.I. Unit of G is Nm²kg^-2

If two bodies of mass 1kg each are separated by 1m from each other then, G = F.

Therefore, universal gravitational constant G is numerically equal to the force of gravitation which exists between two bodies of unit masses kept at a unit distance from each other.

Gravitational force is the weakest force of all.

If two bodies of mass 1kg each are separated by 1m from each other, then, F = G = 6.67*10^-11N

Though the various objects on this earth attracts one another constantly, they do not causes any visible motion because the gravitational force of attraction between them is very, very small.

Imagine a situation on the earth if the object continuously move toward each other due to gravitational force between them.

When both the object are very big, having very large masses, then the gravitational force of attraction between them becomes extremely large.

The gravitational force due to earth on the object of mass 1kg placed on the ground is 9.8 N.

The gravitational force between the earth and the moon even at a large distance is very large and is 2*10²⁰ N.

ohms law, ohms law formulas, what is ohms law, ohms law equations, ohms law definition, define ohms law, Non Ohmic Conductor

noreply@blogger.com (Knowledge world) — Sun, 27 Feb 2022 16:23:00 +0530

Ohm’s Law

The relationship between voltage (V), the current (I) and resistance (R) in a d.c. circuit was first discovered by German scientist George Simon *Ohm. This relationship is called Ohm’s Law and may be stated as under :

The ratio of potential difference (V) between the end of a conductor to the current (I) flowing between them is constant, provided the physical condition ( e.g. temp. And pressure ) do not change i.e.

V/I = Constant = R

Where R is the resistance of the conductor between the point considered.

For example, if in Fig. (a) the voltage between points A and B volts and volts and current flowing is I amp, then v/i will be constant and equal to R, the resistance between points A and B. If the voltage is doubled up, the current will also be doubled up so that the ratio v/i remains constant. If we draw a graph between V and I, it will be a straight line passing through the origin as shown in fig (b). The resistance R between points A and B is given by slope of the graph i.e.

R = tanθ V/I = constant

Ohm’s law can be expressed in three forms

I = V/R ; V = IR ; R = V/I

These formulae can be applied to any part of d.c. circuit or to a complete circuit. It may be noted that if voltage is measured in Volts and current in Amps, then resistance will be in Ohms.

Non Ohmic Conductor

Those conductor which don not obey ohm’s law ( v = IR) are called non ohmic conductor e.g. vacuum tubes, transistor, electrolytes, etc. A non ohmic conductor may have one or more of the following properties:

01. The V - I graph is non linear i.e. V/I is variable.

02. The V-I graph may not pass though the origin as in case of

an ohmic conductor.

03. A non ohmic conductor may conduct poorly or not at all when the p.d. is reversed. The non linear circuit problems are generally solved by graphical methods.

Kirchhoff’s Laws Kirchhoff’s Current Law (KCL) Kirchhoff’s Voltage Law (KVL) Kirchhoff’s Laws derivation

noreply@blogger.com (Knowledge world) — Thu, 24 Feb 2022 19:33:00 +0530

Kirchhoff’s Laws

Kirchhoff’s Circuit Laws are two equalities that deal with the conservation of charge and energy in electrical circuits.

There basically two Kirchhoff’s Law :-

01. Kirchhoff’s Current Law (KCL) - Based on principle of conservation of electric charge.

02. Kirchhoff’s Voltage Law (KVL) - Based on principle of conservation of energy.

Kirchhoff’s Current Law (KCL)

⃝ The rule is also called Kirchhoff’s first law, Kirchhoff’s point rule, Kirchhoff’s junction rule (or nodal rule).

⃝ It states that at the junction, sum of current entering the junction is equal to the sum of current leaving the junction.

Junction is any point in the circuit.

⃝ Consider a case where I1 and I2 are the current entering the junction and,current I3, I4 and I5 are exiting out of the junction.

According to Kirchhoff’s law; I1 + I2 =I3 + I4 + I5

∑ I = 0

Kirchhoff’s Voltage Law (KVL)

⃝ The law is also called Kirchhoff’s second law, Kirchhoff’s loop rule.

⃝ It states that in a closed loop,algebraic sum of Emf is equal to the algebraic sum of product of resistances and respective currents flowing through them.

⃝ Consider a simple circuit having Emf = E1 and E2; R1 and R2 =resistances; current =I1 and I2.

Then according to this law : E1+E2= I1R1+ I2R2

⃝ For example:-

⃝ Consider given figure,let Emfs be E1 and E2 internal resistances be R1, R2 and R3.

⃝ Steps to use Kirchhoff’s law:-

Choose the loop to apply Kirchhoff’s law.

:- Assume any direction.

:- Emf is positive if assumed direction leaving positive terminal of battery.

:- IR is positive if the current in the assumed direction.

:- Consider closed loop ABCDFA, using the assumptions;

:- E2=+R2I3 +R3I2 ;where I3=current flowing through R3

:- Closed loop FCDEF, +E1= +I1R1 + I3R2

:- Closed loop ABDEA, -E1 + E2 = -I1R1 +I2R3

:- If the direction of current is taken opposite then

:- Closed loop ABCDFA ; -E2=-R2I3-R3I2

:- FCDEF; -E1= -I1R1 - I3R2

:- ABDEA; +E1 - E2 = +I1R1 -I2R3

Faraday's Law, Faraday's laws derivation and faraday's Law application and lenz's law

noreply@blogger.com (Knowledge world) — Thu, 24 Feb 2022 19:25:00 +0530

Faraday’s Law of Electromagnetic induction

:- Great experiment physicist and chemist

:- 1791- 1867

:- Contribution to early electricity include:

- Invention of motor, Generator, and Transformer

- Electromagnetic Induction

- Laws of electrolysis: A method of separating bonded element and

Compounds by passing an current through them.

Electromotive Force (EMF) Produced by Changing Magnetic Field, 1

:- A loop of wire is connected to a sensitive ammeter.

:- When a magnet is moved toward the loop, the ammeter deflects.

Electromotive Force (EMF) Produced by Changing Magnetic Field, 2

:- When the magnet is held stationary, there is no deflection of the ammeter.

:- Therefore, there is no induced current

:- Even though the magnet is in the loop.

Electromotive Force (EMF) Produced by Changing Magnetic Field, 3

:- The magnet is moved away from the loop.

:- The ammeter deflects in the opposite direction.

Faraday’s First Law

Faraday’s Law of induction states that “ the emf induced in a circuit is directly proportional to the time rate of change of the magnetic flux through the circuit”

Mathematically,

Faraday’s Second Law

:- Remember ϕB is the magnetic flux through the circuit and is found by

:- If the circuit consists of N loops, all of the same area, and id ϕB is the flux through one loop, an emf is induced in every loop and Faraday’s Law becomes.

Faraday’s Law Example

:- Assume a loop enclosing an area A lies in a uniform magnetic field B

:- The magnetic flux through the loop is ϕB = B.A cos(Φ)

:- The induced emf is

Way of Induced an EMF

:- The magnitude of B can change with time.

:- The area enclosed by the loop can change with time.

:- The angle (Φ) between B and the normal to the loop can change with time.

:- Any combination of the above can occur.

Lenz’s law

:- Faraday’s law indicate that the induced emf and the change in flux have opposite algebraic signs.

:- The has a physical interpretation that has come to be known as Lenz’s Law.

:- Develops by German physicist Heinrich Lenz

Lenz’s Law, cont.

:- Lenz’s Law: - The induced current in a loop is the direction that creates a magnetic field that opposes the change in magnetic flux through the area enclosed by the loop.

:- The induced current tends to keep the original magnetic flux through the circuit from changing.

Application of Faraday’s Law

Electric Generator - An electric conductor, like a copper wire, is moved through a magnetic field, which causes an electric current to flow (be induced) in the conductor.

Generator - Electric generator take in energy by work and transfer it out by electrical transmission.

The ac generator consist of a loop of wire rotated by some external means in a magnetic field.

Application of Faraday’s Law

Pickup coil - The coil is placed near the vibrating string and causes a portion of the string to become magnetized.

When the string vibrate at the same frequency, the magnetized segment produces a changing flux through the coil.

The induced emf is fed to an amplifier.

Application of Faraday’s Law

Transformer - An ac one winding creates a time- varying magnetic flux in the core, which induced a voltage in the other winding.

Application of Faraday’s Law

Yamanashi Maglev - The magnetized coil running along the track, called a guideway, repels the large magnet on the train’s undercarriage, allowing the train to levitate between 0.39 and 3.93 inches ( 1 to 9cm ) above the guideway.

Newton's Law, Acceleration, Velocity, Force

noreply@blogger.com (Knowledge world) — Sat, 15 Jan 2022 10:18:00 +0530

Newton’s Law of Motion

Sir Isaac Newton (1643-1727) an English scientist and mathematician famous for his discovery of law of gravity also discovered the three laws of motion.

Newton’s Laws of Motion

Newton’s First Law: Object in motion tend to stay in motion and objects at rest tend to stay at rest unless acted upon by an unbalanced force.

Newton’s Seconds Law: Force equals mass time acceleration (f = ma).

Newton’s Third Law: For every action there is an equal and opposite reaction.

Newton’s First Law

An object at rest tend to stay at rest and object in motion tends to stay in motion unless acted upon by an unbalanced force.

What does this mean?

Basically, an object will “ keep doing what it was doing ’’ unless acted on by an unbalanced force.

If the object was sitting still, it will remain stationary. If it was moving at a constant velocity, it will keep moving.

It take force to change the motion of an object.

What is mean by unbalance force?

If the forces on an object are equal and opposite, they are said to be balanced, and the object experiences no change in motion. If they are not equal and opposite, then the forces are unbalanced and the motion of the object changes.

Some examples from real life

A soccer ball is sitting at rest. It takes an unbalanced force of a kick to change its motion.

Two teams are playing tug of war. They are both exerting equal forces on the rope in opposite directions. This balanced forces result in no change in motion.

Newton’s First Law is also called the Law of Inertia add to notes

Inertia: The tendency of an object to resist change in its state of motion.

The first law states that all objects have Inertia. The more mass an object has, the more inertia it has (and the harder it is to change its motion).

Newton’s Second Law

Force equals mass times acceleration.

F = ma

Acceleration: A measurement of how quickly an object is changing speed.

What does F = ma mean?

Forces is directly proportional to mass and acceleration.

Imagine a ball of a certain mass moving at a certain acceleration. This ball has a certain force.

Now imagine we make the ball twice a big (double the mass) but keep the acceleration constant. F = ma says that this new ball has twice the force of the old ball.

Now imagine the original ball moving at twice the original acceleration. F = ma says that the ball will again have twice the force of the ball at the original acceleration.

What does F = ma says?

F = ma basically mean that the force of an object comes from its mean and its acceleration.

Something very massive (high mass) that’s changing speed very slowly (low acceleration), like a glacier, can still have great force.

Something very small (low mass) that’s -changing speed very quickly (high acceleration), like a bullet, can still have a great force. Something very small changing speed very slowly will have a very weak force.

Newton’s Third Law

For every action there is an equal and opposite reaction.

Think about it…..

What happens if you are standing on a skateboard or a slippery floor and push against a wall? You slide in the opposite direction (away from the wall), because you pushed on the wall but the wall pushed on the wall pushed back on you with equal and opposite force.

Why does it hurt so much so when you stub your toe? When your toe exerts a force an a rock, the rock exerts an equal forces back on your toe. The harder you hit your your toe against it, the more forces the rock exerts back on your toe ( and the more your toe hurts).

Newton’s Laws of Motion Review

Newton’s First Law: Objects in motion tend to stay in motion and object at rest tend to stay at rest unless acted upon by an unbalanced force.

Newton’s Second Law: Force equals mass time acceleration. (F = ma)

Newton’s Third Law: For every action there is an equal and opposite reaction.

Vocabulary add to notes

Inertia: The tendency of an object to resist change in its state of motion.

Acceleration: ^ A change in velocity.

^ A measurement of how quickly an object is changing, and direction.

Velocity: The rate of changing of a position along a straight line with respect to time.

Force: Push or Pull (strength or energy).

electric dipole and it's derivation, SI unit, and dimensional formula.

noreply@blogger.com (Knowledge world) — Sun, 24 Oct 2021 15:35:00 +0530

Electric Dipole

What is Electric Dipole?

Definition:- It is an arrangement in which two equal and opposite charge are separated by certain distance.

Electrical Dipole Derivation:-

Here two equal and opposite charge -q and +q are placed 2a distance appoint running as electric dipole.

p = q X 2l

Frequently Asked Questions – FAQ’s

What is the SI unit of the dipole moment?

The SI unit of Electrical Dipole is Coulomb.Meter.

Dimensional Formula?

[ L T A ]

Note :- Net charge is zero.

+q-q = 0

Gauss's Theorm , Gauss's law Formula, Gauss's Theorm Proof

noreply@blogger.com (Knowledge world) — Tue, 16 Jun 2020 21:56:00 +0530

Gauss Law states that the total electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity. The electric flux in an area is defined as the electric field multiplied by the area of the surface projected in a plane and perpendicular to the field.

What is Gauss Law?

According to the Gauss law, the total flux linked with a closed surface is 1/ε0 times the charge enclosed by the closed surface.

Mathematically can be expressed as:

For example, A point charge q is placed inside a cube of edge ‘a’. Now as per the Gauss law, the flux through each face of the cube is q/6ε0.

Gauss Law Formula:-

As per the Gauss theorem, the total charge enclosed in a closed surface is proportional to the total flux enclosed by the surface. Therefore, If ϕ is total flux and ϵ0 is electric constant, the total electric charge Q enclosed by the surface is;

Q = ϕ ϵ0

The Gauss law formula is expressed by;

ϕ = Q/ϵ0

Where,

Q = total charge within the given surface,

ε0 = the electric constant.

Gauss's Theorm Proof:-

• Circle Area = 4πr²
• Intensity at point P due to +q charge

• Electrical flux passing through vector da

• Electrical flux passing through the entire surface

Electric flux and Electric Flux derivation

noreply@blogger.com (Knowledge world) — Sat, 13 Jun 2020 23:16:00 +0530

Electric Flux:

" The number of Electric Field lines passing through a certain area is known as Electric Flux through that area."

Note:- Electric Flux is a scalar quantity and electric flux symbol is ∅.

Electric Flux formula Derivation:

Electric flux passing through Vector da

An electrical flux passing through the entire page

Using formula

Electric Flux formula

Electric Flux dimensional formula

Electric Flux unit

Electric Dipole, Electric Dipole Moment, electric dipole moment dimensional formula

noreply@blogger.com (Knowledge world) — Fri, 12 Jun 2020 21:55:00 +0530

Electric Dipole:

An Electric Dipole is a pair of equal and opposite point charges separated by a short distance.

q and -q are two equal and opposite point cahrges saparated by a small distance 2a

Note:- The total charges of the electric dipole is zero, but this does not mean that the field of the electric dipole is zero.

Electric Dipole Moment:

Dipole Moment is a measure of the strength of electric dipole.

Dipole Moment is equal to the product of the magnitude of either charge and the distance between then.

Note:- It is a vector quantity whose direction is from negative charge to positive charge.

S.I. Unit of Electric Dipole Moment = C.m

Electric dipole moment dimensional formula:-

Expression for Electric Field intensity

noreply@blogger.com (Knowledge world) — Thu, 11 Jun 2020 10:48:00 +0530

In this article, we will rigorously derive expressions for the Electric Field due to Point Charge.

Electric Field due to a Point Charge:

Suppose a point charge/ Source charge q is palced at point O.

This charge exerts force F on test charge q0, which is palced at a distance r from it.

From Coulomb's Law

By the definition of Electric Field Intensity

Coulomb's Law value substitute in intensity of electric field

Electric Field Intensity formula is N/C

Where:

Electric Field, Electric Field Intensity, define electric lines of force and its properties

noreply@blogger.com (Knowledge world) — Wed, 10 Jun 2020 00:36:00 +0530

Electric Field:

Electric field due to a given charge is the space around the charge in which electrostatic force of attraction or repulsion due to the charge can be experienced by any other charge.

Source Charge & Test Charge:

The charge which produces electric field is known as source charge.

Charge (generally written as qo) which tests the effect of source charge is called test charge.

what is electric field intensity:

Electric filed intensity at any point is the strength of electric field at that point. It is defined as the force experienced by unit positive charge placed at that point.

Unit of E is NC-1 or Vm-1.

Electric Field Line:

An electric field line is defined as a path, straight or curved in electric field, such that tangent to it at any point gives the direction of electric field intensity at that point.

Properties of Electric Field Lines:

• Electric field lines are continuous curves.

• They start from positively charge and end at negatively charges body.

• Tangent to the electric filed line at any point gives the direction of electric field intensity at that point.

• No two electric field lines intersect each other.

• Electric field lines are always normal to the surface of of a conductor.

Coulomb's Law definition and derivation

noreply@blogger.com (Knowledge world) — Tue, 9 Jun 2020 22:26:00 +0530

Definition:- The magnitude of the electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them.

The law was first published in 1785 by French physicist Charles-Augustin de Coulomb, and was essential to the development of the theory of electromagnetism, maybe even its starting point, because it was now possible to discuss quantity of electric charge in a meaningful way.

Coulomb's Law Derivation:-

We can show it with the following explanation. Let’s say that there are two charges q1 and q2. The distance between the charges is ‘r’, and the force of attraction/repulsion between them is ‘F’. Then

F ∝ q1q2 ••••••• (1)
F ∝ 1/r2 •••••••(2)
By the equation no. 1 and 2

F = k q1q2/ r2
where k is proportionality constant and equals to 1/4 π ε0.

where ε0 is absolute permittivity of free space. Value of this constant in vacuum is 8.85×10−12C2/Nm2. If we put the value of ε0 in above equation for k we find