Magnetic flux

Magnetic flux

·        In electromagnetism, a sub-discipline of physics, the magnetic flux through a surface is the surface integral of the normal component of the field (B) through the surface. It is denoted by Φ or ΦB.

·        The CGS unit is the Maxwell and the SI unit of magnetic flux is the Weber (Wb).

·        Magnetic flux is defined as the number of magnetic field lines passing through a certain closed surface. It measures the total magnetic field that passes through a given area. The region considered here can be of any size and in any direction relative to the direction of the magnetic field. Magnetic flux symbol Magnetic flux is usually indicated by the Greek letter Phi or Phi with the suffix B. Magnetic flux symbol: Φ or ΦB.

Formula of magnetic flux

« The magnetic flux formula is obtained as follows:

Where, ΦB is the magnetic flux.

 B is the magnetic field

 A is the area θ the angle at which the field lines pass through a given area

 Magnetic flux Unit

Magnetic flux is usually measured with a current meter.

«  The SI and CGS unit of magnetic flux is given below: The SI unit of magnetic flux is Weber (Wb). The base unit is volt-seconds.

« The CGS unit is Maxwell

 

 

Understanding Magnetic Flux

«  Faraday's great knowledge was based on the discovery of a simple mathematical relationship that explains many of his experiments on electromagnetic induction. Faraday made many contributions to science and is widely recognized as the greatest experimental scientist of the 19th century.

« Before we can appreciate his work, we must understand the concept of magnetic flux, which plays an important role in electromagnetic induction.

« To calculate the magnetic flux, we consider the image of the line of force of a magnet or magnetic system, as shown in the figure below. The magnetic flux through the plane of the region given by A placed in a uniform field given by B is obtained by the scalar product of the magnetic field and the region A. The angle at which the field lines cross the given area is also important here.

« If the field lines intersect the area at an angle of view, ie     if the angle between the magnetic field vector and the area vector is almost equal to 90ᵒ, then the resulting current is very small.

« When the angle is equal to 0ᵒ, the resulting current is maximum.

           Mathematically,

« Where θ is the angle between vector A and vector B.

« If the field is non-uniform and in different parts of the surface, the field has different magnitude and direction, then the total magnetic flux passing through the given surface can be given as the sum of all such surface elements and their equivalent product. Magnetic field. Mathematically

 It is clear from the above equation that magnetic flux is a scalar quantity.

 Its SI unit is Weber (Wb) or tesla meter squared (Tm2).

 Measurement of Magnetic flux

 The SI unit of magnetic flux is the Weber (Wb) or tesla meter squared (Tm2), named after the German physicist Wilhelm Weber.

 Magnetic flux can be measured with a magnetometer.

Suppose a magnetometer probe is moved over an area of ​​0.6 m2 near a large magnetic material and it shows a continuous reading of 5 mT. The magnetic flux through the area is then calculated as follows: ( 5 × 10-3 T) (0.6 m2 ) = 0.0030 Wb.

If the magnetic field reading changes in an area, it would be necessary to find the average reading.

Magnetic flux Density

Magnetic flux density (B) is the force per unit current per unit length acting on a wire at right angles to the field.

The unit of B is Tesla (T) or B is a vector quantity

 Where

 l = length of the wire,

 F = total force on the wire

 I = current through the wire.

 Faraday's laws of Electromagnetic Induction:

 Faraday's Law of Electromagnetic Induction, also known as Faraday's Law, is a basic law of electromagnetism that helps us predict how a magnetic field interacts with an electric circuit to produce an electromotive force (EMF). This phenomenon is called electromagnetic induction. 

Michael Faraday proposed the laws of electromagnetic induction in 1831. Faraday's law, or law of electromagnetic induction, is an observation or result of Faraday's experiments. He conducted three main experiments to discover the phenomenon of electromagnetic induction

 Faraday's laws of Electromagnetic Induction:

 Faraday's laws of electromagnetic induction consist of two laws.

« The first law describes the emf induction in the conductor and the second law quantifies the emf produced in the conductor.

Experiments of Faraday and Henry Faraday's first law of electromagnetic induction

The discovery and understanding of electromagnetic induction is based on the long experiments of Faraday and Henry. Any change in the magnetic field associated with a coil of wire will cause an emf to be induced in the coil. This emf is called induced emf and if the conductor circuit is closed, current will also circulate through the circuit. This current is called induced current.

 The magnetic field can be changed by following methods:

·        By moving a magnet toward 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.duced when the magnetic flux through the coil changes with time.

Faraday's first law of electromagnetic induction states:

“When a conductor is placed in a changing magnetic field, an electromotive force is induced. When the conductor circuit is closed, a current is induced which is called induced current. To change the strength of the magnetic field in a closed circuit.”

 

Faraday's law Magnetic field strength in a closed circuit

Here are some ways to change the strength of the magnetic field in a closed loop:

·        By rotating the coil relative to the magnet.

·        By moving the coils in or out of the magnetic field.

·        By changing the area of ​​the coil placed in the magnetic field. By moving the magnet towards or away from the coil.

 

Faraday's Second law of Electromagnetic Induction:

Faraday's second law of electromagnetic induction states that "The emf induced in the coil is equal to the rate of change of the year".

The flux linkage is the product of the coil turns and the flux associated with the coil.

The formula of Faraday's law is given below:

 

Where ε is the electromotive force, Φ is the magnetic flux and N is the number of revolutions.

Lenz's Law:

Lenz's law says that" An electromotive force induced by a different polarity induces a current whose field opposes the change in magnetic flux through the circuit to ensure that the original flux is maintained through the circuit as the current passes through it.

Lenz's law, named after Emil Lenz, depends on the principle of conservation of energy and Newton's third law.

This is the most convenient way to determine the direction of the induced current. It states that the direction of the induced current is always such that it opposes the change in the circuit or magnetic field that produces it.

Lenz's law formula

 The law of Lenz is reflected in the formula of the law of Faraday. Here, the negative sign is part of Lenz's law.

The expression is

 

 where, An emf is an induced voltage (also known as an electromotive force). N is the number of loops.

Lenz has many legal applications.

Some of them are listed below –

·        Eddy current balance

·        Metal detectors

·        Dynamometers with current flows

·        Train braking systems

·        Alternating current generators

·        Card readers Microphones

Lenz's law Experiment:

 To find out the induced electromotive force and the direction of the current, we look at Lenz's law. Lenz showed experiments consistent with his theory:

·        Lenz's law First attempt In the first experiment, he concluded that magnetic field lines form when a coil current moves in a circuit. As the current through the coil increases, the magnetic flux increases. The direction of the induced current would be such that it opposes the increase in magnetic flux.

·        One more test In another experiment, he concluded that if a current-carrying coil is wound on an iron bar with the left-hand end behaving N-polarized, and the coil is moved towards S, an induced current is produced.

·        Third attempt In the third experiment, he concluded that if the coil is drawn to the magnetic flux, the coil connected to it shrinks, which means that the area of ​​the coil inside the magnetic field decreases.

·        According to Lenz's law, the motion of the coil is reversed when the induced current is applied in the same direction.   A magnet in a circuit exerts a force to create a current. To resist the change, the current in the magnet must exert a force on the magnet.

 

Experiments of Faraday and Henry

 

In this section, we will learn about the experiments conducted by Faraday and Henry, which are used to understand the phenomenon of electromagnetic induction and its properties

Experiment 1: Experiments of Faraday and Henry In this experiment, Faraday connected a coil to a galvanometer as shown in the figure above.

The bar magnet was pushed towards the coil with the North Pole facing the coil. When the bar magnet is moved, the pointer of the galvanometer deviates, indicating the presence of current in the observed coil. It was found that when the bar magnet is stationary, the pointer shows no deflection and the motion continues only as long as the magnet is moving. Here, the direction of deflection of the pointer depends on the direction of motion of the bar magnet. Likewise, when the south pole of the bar magnet is moved towards or away from the coil, the deflections of the galvanometer are opposite to those observed at the North Pole with similar movements. In addition, the deflection of the pointer is greater or less depending on the speed at which it is pulled toward or away from the coil. The same effect is also observed when moving a coil instead of a bar magnet and holding the magnet in place. This indicates that only the relative motion between the magnet and the coil is responsible for producing current in the coil.

Experiment 2: Experiments of Faraday and Henry In another Experiment,

 

Faraday replaced the bar magnet with a current-carrying coil connected to another battery. Here, the coil current of the connected battery created a uniform magnetic field, making the system analogous to the previous one. As we move from the second coil to the primary coil, the pointer of the galvanometer deviates, indicating the presence of electric current in the first coil. As in the above case, the direction of pointer deflection depends on the direction of movement of the secondary winding towards or away from the primary winding. The amount of deflection also depends on the speed of the coil movement. All these results show that the system in the second case is analogous to the system in the first experiment.

Experiment 3: Experiments of Faraday and Henry

From the above two experiments, Faraday concluded that the relative motion of the magnet and the coil caused the generation of current in the primary coil. But another Faraday experiment showed that relative motion between the coils was not actually necessary to produce a primary current. In this experiment, he placed two fixed coils and connected one of them to a galvanometer using a button and the other to a battery. When the button was pressed, the galvanometer of the second coil showed a deflection, indicating the presence of current in that coil. Also the pointer deflection was temporary and when pressed continuously the pointer showed no curvature and when the key was released the curve was in the opposite direction.

The Left Hand Rule of Fleming and the Right Hand Rule of Fleming

Fleming's Left Hand Rule and Fleming's Right Hand Rule are important rules that apply to magnetism and electromagnetism.

John Ambrose Fleming developed them in the late 19th century as a simple way to determine the direction of electric current in an electric generator or the direction of motion in an electric motor. It is important to note that these rules do not dictate size; instead, show the direction of only three parameters (magnetic field, current, force) when the direction of the other two parameters is known.

What is Fleming's Right Hand Rule?

According to Faraday's law of electromagnetic induction, when a conductor moves through a magnetic field, an electric current is induced in it. Fleming's right hand rule is used to determine the direction of the induced current.

Fleming's Right Hand Rule

Fleming's Right Hand Rule states that if we place the thumb, index finger and middle fingers of the right hand perpendicular to each other, the thumb points in the direction of the conductor's motion relative to the magnetic field, while the index finger indicates that direction magnetic field and the middle finger points in the direction of the induced current.

 What is Fleming's Left Hand Rule?

When a current-carrying conductor is placed in an external magnetic field, a force is applied to the conductor that is perpendicular to both the direction of the field and the direction of the current. Fleming's left-hand rule is used to determine the direction of the force acting on a current-carrying conductor placed in a field.

Fleming's Left-Hand Rule

 Fleming's Left-Hand rule says that if we place the thumb, index finger and middle fingers of the left-hand perpendicular to each other, the thumb will point in the direction of the force experienced by the driver, while the index finger will point in the magnetic direction. direction out and the middle finger points in the direction of the flow.

What are Eddy currents?

 Demonstration:

Have you seen the speedometer inside your car?

In the speedometer, a small magnet is connected to the main shaft of the vehicle. Depending on the speed of the vehicle, it turns. Under the influence of eddy currents, the rotational movement is reversed and the pointer deviates at a certain angle. A pointer attached to a calibrated scale indicates the speed of the vehicle.

 Eddy Current Definition:

When the magnetic flux associated with the coil changes, an electromotive force is induced in the  coil. Eddy currents are so named because the flow looks like eddies . When a conductor is placed in a changing magnetic field, the current induced in the conductor is called current flow. We can define it as:

"Eddy currents are circuits of electric current that are induced inside conductors under the influence of a changing magnetic field in the conductor according to Faraday's law of induction. Eddy currents move in closed circuits within the conductors, in planes perpendicular to the magnetic field".

Like Lenz’s law, there are lots of experiments done to explain the eddy currents. The first test showed that inside a solenoid a soft iron core is introduced and it is connected to the alternating electromotive force. When the metallic disc is placed over the soft iron core, the circuit is switched on and when the circuit is turned on the metallic disc is thrown up away from the iron core.

Uses and applications of Eddy current

Eddy current is widely used in various fields. The most important and widely applied uses are as follows:

·        Induction Furnace – It’s a device used in the smelting industries. The metal to be melted is placed in a rapidly fluctuating high-induced current. The strong induced currents produce a larger amount of heat, and the metal melts. In this way, it’s used in the extraction of metals from the ore.

·        Induction Motor – The induction motor is rotated by employing Eddy currents. It’s done when the induced currents are exposed to the metallic rotor spinning in the magnetic field. So, according to Lenz’s law, the relative motion is reduced between the rotor and the field and rotates in the direction of the magnetic field. Therefore, the induction motor rotates.

·        Energy Metre – In the energy metre, the armature coil has an aluminium disc that rotates in the paired poles of a permanent horseshoe magnet. Due to the braking effect caused by the induced currents, the energy consumed is proportional to the deflection.

·        Speedometer – The speedometer in the vehicle has a magnet that is attached to the main shaft of the vehicle. The magnets are tied with the hair strings. When the vehicle moves, the magnet moves and makes an angle that shows the speed of the vehicle with hair strings.

·        Electric Brakes – In electromagnetic trains, the wheels of the train move in the air, and it can be stopped by electromagnetic currents. The opposite changing flux caused by the Eddy current makes the train stop.

·        Deadbeat Galvanometer – When the induced Eddy current is passed in the coil, without any oscillation, the pointer of the deadbeat galvanometer rests in final equilibrium. This can be done by electromagnetic damping with a large Eddy current.

·        Metal Identification – Detection of counterfeit coins in the coin-operated machines and rejection of the counterfeit coins are done by the Eddy current. When the coin is inserted into the machine, it gets into a stationary magnet, where the eddy current is applied, and validation of the coin takes place.

·        Structure Test – Eddy currents are widely used in structural identification and testing of metallic structures. It’s used to test the structural components of aircraft heat exchange tubes.

·        Inspection – It helps in the inspection of coating layers in metals and products. It’s a non-contact type of inspection, which does not damage the work.

·        Surface Detection – Eddy current is one among the many methods to find the irregularity or discontinuity in the surface of the materials.

 

Motional emf, Electromotive Force, Induced emf

 

We all know that when an electrical conductor is introduced into a magnetic field, due to its dynamic interaction with the magnetic field, EMF is induced in it. This emf is known as induced emf. In this article, we will learn about motional emf where emf is induced in a moving electric conductor in the presence of a magnetic field.

Proof of motional emf

Motional EMF

Consider a straight conductor PQ as shown in the figure, moving in the rectangular loop PQRS in a uniform and time-independent magnetic field B, perpendicular to the plane of the system.

Let us suppose the motion of rod to be uniform at a constant velocity of v m/sec and the surface to be frictionless.

Thus, the rectangle PQRS forms a closed circuit enclosing a varying area due to the motion of the rod PQ.

The magnetic flux ΦB enclosed by the loop PQRS can be given as

ΦB = Blx

 

Where, RQ = x and RS = l, since the conductor is moving, x is changing with time. Thus, the rate of change of flux ΦB will induce an emf, which is given by:

 Where, the speed of conductor (PQ), v = -dx/dt and is the formula of induced emf. This induced emf due to the motion of an electric conductor in the presence of the magnetic field is called motional emf. Thus, emf can be induced in two major ways:

·        Due to the motion of a conductor in the presence of a magnetic field.

·        Due to the change in the magnetic flux enclosed by the circuit.

 

Induced Emf:

It can be defined as the generation of a potential difference in a coil due to the changes in the magnetic flux through it. In simpler words, electromotive force or EMF is said to be induced when the flux linking with a conductor or coil changes.

Electromotive forces can be induced in two different ways

·        The first way involves the placement of an electric conductor in a magnetic field that is varying.

·        The second way involves the placement of a constantly moving conductor in a magnetic field that is static in nature.

The applications of induced emf are,

·        It is used in generators

·        It is used in galvanometers

·        It is used in transformers