Unit-I

Unit-I: (Electromagnetism)

Electromagnetism: Magnetic effect of an electric current, cross and dot conventions, right hand thumb rule, nature of magnetic field of long straight conductor, solenoid and toroid. Concept of mmf, flux, flux density, reluctance, permeability and field strength, their units and relationships. Simple series magnetic circuit, Introduction to parallel magnetic circuit(Only theoretical treatment), comparison of electric and magnetic circuit, force on current carrying conductor placed in magnetic field, Fleming’s left hand rule. Faradays laws of electromagnetic induction, Fleming’s right hand rule, statically and dynamically induced e.m.f., self and mutual inductance, coefficient of couplings. Energy stored in magnetic field.

Introduction to Electromagnetism

Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. The electromagnetic force is carried by electromagnetic fields composed of electric fields and magnetic fields, and it is responsible for electromagnetic radiations such as light.

What is Magnet?

An object which is capable of producing magnetic field and attracting unlike poles and repelling like poles.

Properties of Magnet

Following are the basic properties of magnet:

When a magnet is dipped in iron filings, we can observe that the iron filings cling to the end of the magnet as the attraction is maximum at the ends of the magnet. These ends are known as poles of the magnets.
Magnetic poles always exist in pairs.
Whenever a magnet is suspended freely in mid-air, it always points towards north-south direction. Pole pointing towards geographic north is known as the North Pole and the pole pointing towards geographic south is known as the South Pole.
Like poles repel while unlike poles attract.
The magnetic force between the two magnets is greater when the distance between these magnets are lesser.
Magnetic Induction

Types of Magnets

There are two types of magnets, and they are as follows:

Permanent magnet (Natural Magnet)
Electromagnets

Permanant Magnet (Natural Magnet)

Permanent magnets are those magnets that are commonly used. They are known as permanent magnets because they do not lose their magnetic property once they are magnetized.

Electromagnets

Electromagnets consist of a coil of wire wrapped around the metal core made from iron. When this material is exposed to an electric current, the magnetic field is generated making the material behave like a magnet. The strength of the magnetic field can be controlled by controlling the electric current.

Magnetic Induction

The process by which a substance, such as iron or steel, becomes magnetized by a magnetic field. The induced magnetism is produced by the force of the field radiating from the poles of a magnet.

First Law of Magnetism

1^st Law states that the unlike pole attract each other and like pole repel each other.

Second Law of Magnetism

It’s state that force exerted by one pole to the another pole is directly proportional to the product of the pole strength of the 2 pole and inversely proportional to the square of distance between them.

F=kq1q2/r2

Magnetic Field

Magnetic field is an invisible space around a magnetic object. A magnetic field is basically used to describe the distribution of magnetic force around a magnetic object.

Magnetic fields are created or produced when the electric charge/current moves within the vicinity of the magnet. Here, the sub-atomic particle such as electrons with a negative charge moves around creating a magnetic field. These fields can originate inside the atoms of magnetic objects or within electrical conductors or wires.

Magnetic Lines of Force

It is an imaginary lines which is use to represent the magnet field.

Magnetic flux(Ø)

Magnetic flux is defined as the number of magnetic field lines passing through a given closed surface. It provides the measurement of the total magnetic field that passes through a given surface area. Here, the area under consideration can be of any size and under any orientation with respect to the direction of the magnetic field.

Magnetic flux density(B)

The magnetic flux density is defined as the amount of magnetic flux through a unit area placed perpendicular to the direction of magnetic field. It is a vector quantity, usually denoted by B. The SI unit of magnetic flux density is Tesla (T).

Magnetic flux Strength(H)

It is define as the force experienced by unit north pole placed at the point in the magnetic field.

Magnetic field strength is one of two ways that the intensity of a magnetic field can be expressed. Technically, a distinction is made between magnetic field strength H, measured in amperes per meter (A/m), and magnetic flux density B, measured in Newton-meters per ampere (Nm/A), also called teslas (T).

Magnetive Motive Force (MMF)

Magnetomotive Force Definition: The current flowing in an electric circuit is due to the existence of electromotive force similarly magnetomotive force (MMF) is required to drive the magnetic flux in the magnetic circuit. The magnetic pressure, which sets up the magnetic flux in a magnetic circuit i s called Magnetomotive Force.

MMF=N*I

Reluctance (S)

Magnetic reluctance (also known as reluctance, magnetic resistance, or a magnetic insulator) is defined as the opposition offered by a magnetic circuit to the production of magnetic flux. It is the property of the material that opposes the creation of magnetic flux in a magnetic flux.

Fleming's Left Hand Rule

Fleming's Left Hand Rule. Whenever a current carrying conductor is placed in a magnetic field, it experiences a force due to the magnetic field. The direction of force acting on the conductor can be found out using Fleming's Left Hand Rule.

According to Fleming's left hand rule, if the thumb, fore-finger and middle finger of the left hand are stretched to be perpendicular to each other as shown in the illustration at left, and if the fore finger represents the direction of magnetic field, the middle finger represents the direction of current, then the thumb represents the direction of force.

Dot and Cross Convention

If current flowing through the conductors is moving towards the observer and out of the plane of paper.It is denoted by Dot Convention
Generally the tip of arrow indicates the direction of current.
If current flowing through the conductors is moving away from the observer and out of the plane of paper.It is denoted by Cross Convention
Generally the tail of arrow indicates the direction of current.

Cork screw Rule

Maxwell's screw rule : If a right handed cork screw is assumed to be held along the conductor, and screw is rotated such that it moves in the direction of the current, direction of magnetic field is same as that of the rotation of screw. It is also known as Maxwell's corkscrew rule or Right handed corkscrew rule.

Permeability

It is defined as the ability of the material to carry flux lines.
If material allow flux lines to pass through it easily then material having high permeability.
If material does not allow flux lines to pass through it easily then material having low permeability.

There are 2 types of permeability.

1)Absolute permeability

2)Relative permeability

1) Absolute permeability

It is the ratio of magnetic flux density (B) in a particular medium to the magnetic field strength (H) which produces that flux density.

2) Relative permeability

It is the ratio of magnetic flux density (B) in a particular medium produce by magnet to the flux density in air or vacuum

Magnetic Field Strength due to long conductors

MAGNETIC FIELD PATTERN DUE TO STRAIGHT CURRENT-CARRYING CONDUCTOR

The region around a magnet where magnetism acts is represented by the magnetic field.
The force of magnetism is due to moving charge or some magnetic material.
Like stationary charges produce an electric field proportional to the magnitude of charge, moving charges produce magnetic fields proportional to the current. In other words, a current carrying conductor produces a magnetic field around it. The sub-atomic particles in the conductor like the electrons moving in atomic orbitals are responsible for the production of magnetic field.
The magnetic field lines around a straight conductor (straight wire) carrying current are concentric circle whose centres lie on the wire.

DISCOVERY OF MAGNETIC FIELD BY CURRENT CARRYING CONDUCTOR

During the early 19th century, a scientist named H. C. Oersted discovered that a current carrying conductor produces magnetic effect around it.
Also, effect of lightning striking a ship caused the malfunctioning of compass needles, disrupting the navigation system. This was the basis for establishment of a relationship between moving electric charge or current and magnetic field.

FACTOR ON WHICH THE MAGNETIC FIELD PRODUCED:

Magnetic field is directly proportional to the current passing through the wire and it is inversely proportional to the distance from the wire.

DETECTING DIRECTION OF MAGNETIC FIELD: RIGHT HAND THUMB RULE

While grasping (or holding) the current-carrying wire in your right hand so that your thumb points in the direction of current, then the direction in which your fingers encircle the wire will give the direction of magnetic field lines around the wire.

Magnetic Field Due to Solenoid

A coil of wire which is designed to generate a strong magnetic field within the coil is called a solenoid. Wrapping the same wire many times around a cylinder creates a strong magnetic field when an electric current is passed through it. N denotes the number of turns the solenoid has. More the number of loops, stronger is the magnetic field.

A solenoid is a type of electromagnet whose intention is to produce a controlled magnetic field. If the purpose of a solenoid is to impede changes in the electric current, it can be more specifically classified as an inductor.

The formula for the magnetic field of a solenoid is given by,

Please note that the magnetic field in the coil is proportional to the applied current and number of turns per unit length.

Magnetic field due to toroid

A toroid is a long solenoid which is bend into circular form. So, toroid is equivalent to the solenoid having infinite length but it has finite no. of circular turns. Consider a toroid having radius r, carrying current I through it. If N is the number of turns in toroid and n be the no. of turns per unit length then

Magnetic effect of electric current

When current pass through a conductor magnetic field generated.
If the current is DC, then the associated magnetic field is stationary.
If the current is AC, then the associated magnetic field is varying w.r.t time.

Right hand thumb rule

If the straight conductor is held in the right hand such that the thumb indicates the direction of current and curd fingers indicate direction of magnetic field.

Force on current carrying conductors placed in magnetic field

If we are placed current carrying conductor in a magnetic field, following sequence take place.

1)Development of Individual Fields.

2)Interaction of 2 Magnetic Field.

3)Force Exerted on the conductor.

1)Development of Individual Fields

Straight conductor placed in a magnetic field produced by magnet.
Let the current flowing through the conductor be out of the plane of the paper i.e. towards the user , current direction denoted by dot convention.

2) Interaction of 2 Magnetic Field

Due to presence of 2 magnetic fields simultaneously, interaction take place between them.
Flux lines produced by magnet and conductor are in opposite direction to each other at the top and hence cancel each other. The number of flux line decrease at the top.
At the bottom, the individual fields are in same direction, hence fields add each other. The number of flux line increase at the bottom.

3) Force Exerted on the conductor.

As we know that the properties of line of force act as stretched elastic bands and always try to contract in length
The lines of force at the bottom will exert a force on the conductor in the upward direction.
Hence force is exerted on the conductor from the high flux line area towards the low flux area.

Faraday’s Laws of Electromagnetic Induction: First & Second Law

What is Faraday’s Law

Faraday’s law of electromagnetic induction (referred to as Faraday’s law) is a basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF). This phenomenon is known as electromagnetic induction.

Faraday’s law states that a current will be induced in a conductor which is exposed to a changing magnetic field. Lenz Law of Electromagnetic Induction states that the direction of this induced current will be such that the magnetic field created by the induced current opposes the initial changing magnetic field which produced it. The direction of this current flow can be determined using Fleming Left Hand Rule.

Faraday’s law of induction explains the working principle of transformer, motor, generator and inductors. The law is named after Michael Faraday, who performed an experiment with a magnet and a coil. During Faraday’s experiment, he discovered how EMF is induced in a coil when the flux passing through the coil changes.

Faraday’s First Law

Any change in the magnetic field of a coil of wire will cause an emf to be induced in the coil. This emf induced is called induced emf and if the conductor circuit is closed, the current will also circulate through the circuit and this current is called induced current.

Method to change the magnetic field:

By moving a magnet towards or away from the coil
By moving the coil into or out of the magnetic field
By changing the area of a coil placed in the magnetic field
By rotating the coil relative to the magnet

Faraday’s Second Law

It states that the magnitude of emf induced in the coil is equal to the rate of change of flux that linkages with the coil. The flux linkage of the coil is the product of the number of turns in the coil and flux associated with the coil.

Fleming's right-hand rule

Fleming's right-hand rule (for generators) shows the direction of induced current when a conductor attached to a circuit moves in a magnetic field. It can be used to determine the direction of current in a generator's windings.

When a conductor such as a wire attached to a circuit moves through a magnetic field, an electric current is induced in the wire due to Faradays law of Induction. The current in the wire can have two possible directions. Fleming's right-hand rule gives which direction the current flows.

The right hand is held with the thumb, index finger and middle finger mutually perpendicular to each other (at right angles), as shown in the diagram.

The thumb is pointed in the direction of the motion of the conductor relative to the magnetic field.
The first finger is pointed in the direction of the magnetic field. (north to south)
Then the second finger represents the direction of the induced or generated current within the conductor (from + to -, the terminal with lower electrical potential to the terminal with higher electric potential, as in a voltage source)

The bolded letters in the directions above give a mnemonic way to remember the order. Another mnemonic for remembering the rule is the initialism "FBI", standing for Force (or otherwise motion), B the symbol for the magnetic field, and I the symbol for current. The subsequent letters correspond to subsequent fingers, counting from the top. Thumb -> F; First finger -> B; Second finger -> I.

Statically and Dynamically Induced EMF

Induced e.m.f can be either dynamically induced emf or statically induced emf. in this first case, usually the field is stationary and conductors cut across it (as in d.c. generator). But in the second case, usually the conductor or the coil remains stationary and flux linked with it is changed by simply increasing or decreasing the current producing this flux (as in transformers).

Dynamically Induced EMF

We have learnt that when the flux linking with the coil or circuit changes, an emf is induced in the coil or circuit.

EMF can be induced by changing the flux linking in two ways:

By increasing or decreasing the magnitude of the current producing the linking flux. In this case, there is no motion of the conductor or of coil relative to the field and, therefore, emf induced in this way is known as statically induced
By moving a conductor in a uniform magnetic field and emf produced in this way is known as dynamically induced emf

Fig. 4 illustrates another way of determination of induced emf, known as right hand flat palm rule. This law states that if right hand is so placed in a magnetic field along the conductor that the magnetic lines of force emerging from the north pole enter the palm and the thumb points in the direction of motion of conductor, the other four fingers will give the direction of induced emf or current.

STATICALLY INDUCED EMF

Statically induced emf may be (a) self-induced emf or (b) mutually induced emf

Self-Induced EMF

When the current flowing through the coil is changed, the flux linking with its own winding changes and due to the change in linking flux with the coil, an emf, known as self-induced emf, is induced.

Since according to Lenz’s law, an induced emf acts to oppose the change that produces it, a self-induced emf is always in such a direction as to oppose the change of current in the coil or circuit in which it is induced. This property of the coil or circuit due to which it opposes any change of the current in the coil or circuit, is known as self-inductance.

Consider two coils A and B placed closed together so that the flux created by one coil completely links with the other coil. Let coil A have a battery and switch S and coil B be connected to the galvanometer G.

When switch SW1 is opened, no current flows through coil A, so no flux is created in coil A, i.e. no flux links with coil B, therefore, no emf is induced across coil B, the fact is indicated by galvanometer zero deflection. Now when the switch S is closed current in coil. A starts rising from zero value to a finite value, the flux is produced during this period and increases with the increase in current of coil A, therefore, flux linking with the coil B increases and an emf, known as mutually induced emf is produced in coil B, the fact is indicated by galvanometer deflection. As soon as the current in coil A reaches its finite value, the flux produced or flux linking with coil B becomes constant, so no emf is induced in coil B, and galvanometer pointer returns back to zero position. Now if the switch S is opened, current will start decreasing, resulting in decrease influx linking with coil B, an emf will be again induced but in direction opposite to previous one, this fact will be shown by the galvanometer deflection in opposite direction.

Hence whenever the current in coil A changes, the flux linking with coil B changes and an emf, known as mutually induced emf is induced in coil B.

Coefficient of Mutual Induction

Mutual inductance may be defined as the ability of one coil or circuit to induce an emf in a nearby coil by induction when the current flowing in the first coil is changed. The action is also reciprocal i.e. the change in current flowing through second coil will also induce an emf in the first coil. The ability of reciprocal induction is measured in terms of the coefficient of mutual induction M.

The coefficient of mutual induction (M) can be determined from any one of the following three relations.

First Method. In case the dimensions of the coils are given, the coefficient of mutual induction may be determined from the relation

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