# Chapter 4: Magnetic Effects of Electric Current Notes

## Magnetic Field Definition

According to the definition of the magnetic field, it is the region around a magnet or current-carrying conductor around which the force of magnetism can be observed.

It is a vector quantity and is generated by moving charges. Magnetic forces and Electric forces are part of one of the four fundamental forces of nature. Electric and Magnetic forces interplay with each other to form electromagnetic forces which are an essential part of our modern engineering infrastructure and development.

## Unit of Magnetic Field

The SI unit for the magnetic field is the tesla (T).

• B-Field: It is the magnetic field defined by the force it exerts on a moving charged particle.
• H-Field: It is defined as the magnetic field within a material, rather than in a vacuum.

B-Field is measured in Tesla (T) while H-Field is measured in Ampere/meter (A/m). In the CGS system, the unit of measurement for the B-field is the gauss (G), (1 T = 10000 G), while the H-field is measured in Oersted (Oe) (1 Oersted = 1000/4π A/m ≈ 79.577 A/m).

## Illustration of Magnetic Field

A Magnet is a material that has the ability to produce a magnetic field which creates magnetic field lines, the field force is able to attract and repel other ferromagnetic materials like iron, nickel, etc. The magnetic field can be illustrated using two possible ways – Magnetic Field Vector and Magnetic Field Lines.

### Magnetic Vector Field

The magnetic field is a vector quantity (it has both magnitude and direction), and the direction of the magnetic field is from the north pole to the South Pole. It is a vector field, mathematically which means it is a set of many vectors which points in different directions. The figure below illustrates a magnetic field using a magnetic field vector. The length of these vectors determines the strength of the field at that particular point.

## Magnetic Field Lines

Another representation of the magnetic field can be done using the magnetic field lines which are shown in the figure below. The strength of the magnetic field is shown here by the closeness of magnetic field lines. For example, the magnetic field is stronger at the poles because the lines are more crowded in that area.

### Properties of Magnetic Field Lines

Some of the properties of magnetic field lines are as follows:

• Magnetic Field lines never cross each other.
• Tangent to magnetic field lines gives the direction of the magnetic field.
• The density of field lines is directly proportional to the strength of the field
• Field lines always form a closed loop.
• Field lines emerge from the north pole and terminate at the south pole.
• Inside the magnet, the direction of field lines is reversed, flowing from south to north.
• Magnetic field lines have both direction and magnitude, represented by a vector.
• The magnetic field is stronger at poles due to denser field lines.

## Magnetic Field Intensity

Magnetic field Intensity denotes the strength of the magnetic field. It is represented by H and is a vector quantity. It is defined as the magnetomotive force(MMF) needed to create a flux density B inside a material per unit length of that material. The unit of Magnetic Field intensity is Ampere/Meter and the dimensional formula for the same is given by [M1T-2I-1]. SI unit of Magnetic Field Intensity is Tesla.  A magnetic field of strength One Tesla can also be thought of as the magnetic field producing a force of 1 Newton per ampere of current in each meter of conductor.

H = B/μ – M

here,

• B is the Magnetic Flux Density
• M is Magnetization
• μ is Magnetic Permeability

### Magnetic Effect of Electric Current

When current is passed through a magnetic material, a magnetic field is produced, if a needle is placed near the material, providing the electric charge (moving charges), the needle will deflect. The area to the point where the force is exerted by the magnetic material is called a magnetic field.

## Magnetic Field lines due to Current Carrying Straight Conductor

The magnetic field lines produced by a straight current-carrying conductor is in the form of concentric circles, depending upon the direction of the current, magnetic field lines also change their directions.

The direction of the magnetic field lines can be identified by

• Right-hand Thumb Rule
• Maxwell’s Corkscrew Rule

Let’s understand these rules in detail as follows:

### Right-Hand Thumb Rule

According to Right- Hand Thumb Rule, If the right hand’s thumb is placed in the direction of the moving current, then the direction of the fingers shows the direction of magnetic field lines, Similarly, if the thumb is placed in the direction of the magnetic field lines, then the direction of current is shown by the curled fingers’ direction.

### Maxwell’s Corkscrew Rule

According to Maxwell’s Corkscrew rule, A screw can tell the direction of the magnetic field lines. If the screw is moved forward, the direction of rotation shows the direction of magnetic field lines while the direction of the movement of the screw shows the direction of current and Vice-Versa.

## Magnetic Field lines due to Current through a Circular Loop

The magnetic field lines will create the same pattern as they created in the case of a straight current-carrying conductor, That means, the field lines will be concentric in nature, but based on the direction of the current, the direction of field lines will change as well. For example, in a circular loop, imagine two places, one where the current goes upward and one where the current goes downward, according to the right-hand thumb rule, in the first case, the field lines must be anticlockwise in nature, and in the second case, the field lines must be clockwise in nature.

## Magnetic Field lines due to Current in Solenoid

A solenoid is a helical coil which upon giving current becomes an electromagnet and forms the North and South Pole and due to moving charges, it creates Magnetic field lines. The field lines created by the solenoid look similar to the field lines created by a simple Bar magnet.

## Force on a current-carrying conductor placed in a Magnetic Field

Imagine a wire (conductor) is placed under a magnet and current is passed through the wire, due to the moving electric charges in a magnetic field, a force is applied to the conductor that moves it in a certain direction, this phenomenon was given by Michael Faraday. The direction of the force on the conductor is determined by Fleming’s left-hand rule.

### Fleming’s Left-hand Rule

According to Fleming’s left-hand rule, the direction of force can be determined with the help of the left hand’s thumb, index finger, and middle finger. The thumb represents the Force, The index finger shows the direction of the magnetic field lines and the middle finger shows the direction of the current. Therefore, if the middle finger and index finger are kept in the direction of current and magnetic field lines respectively, the thumb will represent the direction of force produced on the current-carrying conductor.

## Difference between Magnetic Field and Electric Field

There are some key differences between Magnetic Field and Electric Field, which are listed in the following table:

The magnet is mainly divided into three categories that are:

1. Permanent magnet – A magnet made from a material that is permanently magnetized and creates its own consistent magnetic field. Materials that can be magnetized are called ferromagnetic. Examples of such materials are iron, nickel, and cobalt.
2. Temporary magnet – Magnet that remains magnetized for a short period of time. Materials used to make these magnets are generally soft materials having low magnetic properties. When a strong or permanent magnet attracts them, they become magnetized for a short duration.
3. Electromagnet – A magnet in which a magnetic field is produced by the current flowing in it. The most common electromagnet is the wire wound into a coil; when current flows through the wire, a magnetic field is created inside the coil. It disappears as soon as the current is cut off. Electromagnets are mainly used in devices such as motors, generators, and hard disks.

Magnetism is the force of pull or push when two magnets are kept in each other’s vicinity.

### Magnetic Fields due to Moving Charges

Moving charges produce a magnetic field. In a conductor carrying current, charges are always moving and thus such conductors produce magnetic fields around them. The field that is produced by these charges can be visualized in the figure below. The direction of this magnetic field is given by the right-hand thumb rule. In this rule, the thumb of the right-hand points in the direction of the current. The curled fingers give the direction of the magnetic field around the wire.

The magnetic fields produced by a current loop and solenoid are shown in the figure below:

### Biot-Savart Law

Biot-Savart law establishes the relationship between the electric current and the magnetic field produced by it. The figure shown below shows a current-carrying conductor in space. Let us denote the current that the conductor is carrying by “I”. Consider “dl” as an infinitesimally small part of the conductor. Then, the magnetic field dB at a point P due to this current carrying element at distance “r” will be given by,

The closeness of field lines shows the relative strength of the magnetic field, i.e. closer lines show a stronger magnetic field and vice—versa. Crowded field lines near the poles of the magnet show more strength.

Some important properties of magnetic field lines are:

• Magnetic field boundaries are never crossed.
• The depth of the field lines shows the field’s power.
• Magnetic field lines are often closed loops.
• Magnetic field lines often originate from or begin at the north pole and end at the South Pole.

## Magnetic Field Due to Current Carrying Conductor

When current is passed through a straight current-carrying conductor, a magnetic field is produced around it. The field lines are in the form of concentric circles at every point of the current-carrying conductor. And we can find the direction of the magnetic field, in relation to the direction of electric current through a straight conductor can be depicted by using the Right-Hand Thumb Rule also called as Maxwell Corkscrew Rule.

This rule states that ‘If a current-carrying conductor is held by the right hand, keeping the thumb straight and if the direction of electric current is in the direction of thumb, then the direction of wrapping of other fingers will show the direction of the magnetic field.’

### Magnetic field due to current through a circular loop

The right-hand thumb rule can be used for a circular conducting wire as well as it comprises small straight segments. Every point on the wire carrying current gives rise to a magnetic field around it would become larger and larger as we move away from the wire and by the time we reach the center of the circular loop, the arcs of these circles would appear as a straight line

### Magnetic field and number of turns of the coil

The magnitude of the magnetic field gets summed up with the increase in the number of turns of the coil. If there are ‘n’ turns of the coil, the magnitude of the magnetic field will be ‘n’ times the magnetic field in case of a single turn of the coil.

The strength of the magnetic field at the center of the loop (coil) depends on:

• The radius of the coil: The strength of the magnetic field is inversely proportional to the radius of the coil. If the radius increases, the magnetic strength at the center decreases
• The number of turns in the coil: As the number of turns in the coil increase, the magnetic strength at the center increases, because the current in each circular turn is having the same direction, thus, the field due to each turn adds up.
• The strength of the current flowing in the coil: As the strength of the current increases, the strength of three magnetic fields also increases.

## Characteristics of Magnetic Field Due To Current Carrying Conductor

Following are the characteristics of the Magnetic Field due to Current Carrying Conductor:

• The lines of force near the wire are almost concentric circles.
• Moving toward the center of the loop, the concentric circles become larger and larger.
• Near the center of the loop, the arcs of these big circles appear as parallel straight lines.
• The magnetic field is almost uniform at the center of the loop.
• The magnitude of the magnetic field produced by a current-carrying circular loop (or circular wire) at its center is:
• Directly proportional to the current passing through the circular loop (or circular wire), and
• Inversely proportional to the radius of the circular loop (or circular wire).

## FAQs on Magnetic Field due to Current Carrying Conductor

Question 1: Explain the effect on the magnetic field produced at a point in a current-carrying circular coil due to an increase in the amount of current flowing through it.

The magnetic field produced by current carrying circular coil is directly proportional to the current flowing through the coil. Therefore, with increase in the magnitude of magnetic field the current flowing through the coil will increase.

Question 2: How does a Solenoid behave like a Magnet?

Since solenoid has iron core with insulated copper wire around it, therefore it behaves like magnet. When a current is flowing through the solenoid, magnetic field is produced around it. And the field produced is similar to the magnetic field of a bar magnet.

Question 3: Define the right-hand thumb rule.

This rule states that ‘If a current carrying conductor is held by right hand, keeping the thumb straight and if the direction of electric current is in the direction of thumb, then the direction of wrapping of other fingers will show the direction of magnetic field.’

Question 4: Why don’t two magnetic field lines cannot intersect each other?

All Field lines follow their own path to reach from the North Pole to the South Pole. Two magnetic field lines do not intersect each other because if there was point of intersection, then there would be two tangents for a single point which means that the magnetic field has two directions, which is not possible.

Question 5: What is a Solenoid?

The solenoid is the coil with many circular turns of insulated copper wire wrapped closely in the shape of a cylinder. A current-carrying solenoid produces a similar pattern of the magnetic field as a bar magnet. One end of the solenoid behaves as the North Pole and another end behaves as the South Pole.

### Solenoid

The solenoid is a wire coil that works as an electromagnet when electricity flows through it. Electromagnetic solenoids are used in a variety of applications across the world.

It’s nearly impossible to swing a bat without striking a solenoid. Solenoids are found in both speakers and microphones. In reality, a speaker and a microphone are essentially the same things when seen from the opposite perspective. Solenoids are used in a variety of solenoid engines because the coils may be reinforced by adding an iron core. Solenoids, like bar magnets, are made up of a large coil of wire wrapped in many turns that generates a homogeneous magnetic field when electricity is delivered through it.

Applications of Solenoid

They’re suitable for a certain type of door locking mechanism. Electromagnets are used in these locking systems, making them extremely secure.

• It has a wide range of applications, including medical, industrial, locking systems, and automotive.
• They’re utilized in inductors, valves, and antennas, among other things.
• In automobiles, solenoids are utilized in fuel injection gears.
• The solenoid is mostly used as a power switch.
• They’re commonly seen in computer printers.
• It is used to electronically operate a valve.

• A solenoid offers a number of benefits that you won’t find in a regular coil:
• When electricity is introduced to a solenoid, it causes it to respond instantly.
• There is no pollution in the air when a solenoid engine is used in vehicles.
• Solenoid engines can be utilized to replace fossil fuel engines.

### Force on a Moving Charge in a Magnetic Field

Consider the figure below, this figure shows a conductor that is under the influence of a magnetic field. The conductor is connected to a battery that is continuously causing the current to flow in the wire and the conductor. Since the charges are moving inside the conductor, these charges start experiencing force. Now, these charges are in the conductor and cannot go outside, so the force exerted on these charges is in turn transferred to the force being applied on the conductor.

The direction of the force experienced by the conductor is given by the right-hand thumb rule. Now let’s focus on deriving the formula for calculating the force on a current-carrying conductor.

### What is an Electric Motor?

An electric motor is a machine that is used to convert electrical energy into mechanical energy. When a current-carrying conductor is placed in the magnetic field it experiences some forces that help in the rotation of the shaft or axil.

A motor is a piece of machinery that transforms electrical energy into mechanical energy. A mixer, for example, has spinning blades that mash and combine ingredients. The electric energy input to the mixer is converted into mechanical energy of the blade rotating, resulting in the desired action.

### Principle of an Electric Motor

• A motor operates on the principle of the current magnetic effect. When a current-carrying conductor generates a magnetic field around it then a force acts on a current-carrying conductor when it is placed perpendicular to the magnetic field.
• When a rectangular coil is put in a magnetic field and current is transmitted through it, a force acts on the coil, causing it to spin continuously.
• Consider the poles of two bar magnets held facing each other, separated by a narrow escape. A small length of conducting wire is formed into a loop and placed in the gap between the magnets so that it is in the magnetic field created by the magnets. As the loop’s ends are wired to the battery terminals, the loop begins to spin. This is due to the magnet’s magnetic field interfering with the electric current passing into the conductor. The induced South Pole is drawn to the North Pole due to the magnetic poles induced in the circle, and vice versa. As the current in the circle reverses, the caused the South Pole becomes the North Pole and is drawn to the magnet’s south pole. This leads the circle to spin indefinitely.

Fleming’s Left-Hand Rule

The first finger, middle finger, and thumb of your left hand should be stretched perpendicular to each other in such a way that the first finger represents the direction of the magnetic field, the middle finger represents the direction of the current in the conductor, and the thumb indicates the direction of motion of the conductor, according to Fleming’s left-hand rule.

### Construction of an Electric Motor

Construction of an Electric Motor

Following are the main parts of the motor as shown in the figure above, with their respective functions:

1. Battery: A Battery is the DC power source that is frequently connected to a basic motor. It supplies DC current to the armature coil.
2. Brushes: There are two carbon brushes present in the electric motor which serve as a connection between the commutator and the battery terminals.
3. Permanent magnet: generates a strong magnetic field.
4. Split ring type commutator: The reversal of current in the armature coil is takes place with the help of the commutator. It is made up of two metallic ring halves. The armature coil’s two ends are connected to these two halves’ metallic ring.
5. Armature core: The armature coil is held in place by the armature core and also provides mechanical support to the coil.
6. Armature coil: It is made up of single or multiple rectangle-shaped loops of insulated copper wire.
7. Axle or Shaft: It is the place where the exchange of mechanical power takes place. The armature core and the commutator are mounted on the shaft.

### Working of an Electric Motor

Working of an Electric Motor

1. Initially, Brush B1 makes contact with the commutator half-ring R1, whereas brush B2 makes contact with the commutator half-ring R2. Current flows from A to B along coil side l1 of the rectangular coil ABCD, and from C to D along coil side l2. The magnetic field is directed from the magnet’s North pole to its South pole.
2. The force F on the coil side l1 of the coil is in a downward direction, but the force F on the coil side l2 of the coil is in an upward direction, according to Fleming’s Left-hand rule. As a result, the coil’s side l1 is pulled down while its side l2 is pushed up. This causes the coil ABCD to revolve counterclockwise.
3. When the coil reaches a vertical position while rotating, the brushes will contact the gap between the two commutator rings which cut off the flow of the current i in the coil. Despite the fact that the current i to the coil is cut off when it reaches the exact vertical position, the coil continues to rotate because it has momentum and has moved beyond the vertical position.
4. When the coil moves beyond the vertical position after the half revolution, the coil’s side l2 moves to the left, while the coil’s side l1 moves to the right, and the two commutator half rings automatically change contact position from one brush to the other that is Brush B1 makes contact with the commutator half-ring R2, whereas brush B2 makes contact with the commutator half-ring R1. This makes the coil’s current i flow in the other direction.
5. Now, the force acting on the sides l1 and l2 of the coil is reversed when the current direction is reversed. The coil’s side l2 is now on the left, with a downward force applied to it, while the side lis now on the right, with an upward force F applied to it. As a result, the coil’s side l2 is pulled down and the coil’s side l1 is pushed up. This causes the coil to rotate counterclockwise.
6. After every half rotation, the current in the coil is reversed, and the coil continues to revolve as long as electricity from the battery is transmitted through it.

### Uses of an Electric Motor

Electric motors are utilized for a wide range of purposes. The following is a list of some of them.

1. Electric cars: Electric cars used in traveling. and it is pollution-free.
2. Rolling mills: Rolling mills used to decrease the width of the hard material like metals.
3. Electric cranes: Electric cranes used to lift heavy objects.
4. Lifts: Basically used in big buildings.
5. Drilling machine: A drilling machine used to make a hole in the walls or woods
6. Fan: Fans are used for blowing air.
7. Hairdryers: Hairdryers used to dry wet hair.
8. Tape recorder: A tape recorder used to record the audio or video.
9. Washing machine: The washing machine is the wash the clothes.
10. Mixers: Mixers are used to mash and mix things.

The efficiency of a motor to be roughly about 70 – 85% as the remaining energy is wasted in heat production and sounds emitted.

### Sample Problems

Problem 1: State Fleming’s left-hand rule.

Solution:

Fleming’s left-hand rule state that the first finger, middle finger, and thumb of your left hand should be stretched perpendicular to each other in such a way that the first finger represents the direction of the magnetic field, the middle finger represents the direction of the current in the conductor, and the thumb indicates the direction of motion of the conductor, according to Fleming’s left-hand rule.

Problem 2: What is the principle of an electric motor?

Solution:

A motor operates on the principle of the current magnetic effect. When a current-carrying conductor generates a magnetic field around it then a force acts on a current-carrying conductor when it is placed perpendicular to the magnetic field.

Problem 3: What is the role of the split ring in an electric motor?

Solution:

The reversal of current in the armature coil takes place with the help of the commutator. It is made up of two metallic ring halves. The armature coil’s two ends are connected to these two halves metallic ring.

Problem 4: How will you find out the direction of the magnetic field produced by the current-carrying conductor?

Solution:

Maxwell’s right-hand thumb rule is used to determine the direction of the magnetic field lines created by a straight wire carrying electricity. Imagine that the current-carrying wire is in the right hand, with the thumb pointing in the direction of the current, and the direction in which the fingers encircle the wire determines the direction of magnetic lines of force around the wire.

Problem 5: What is the difference between a bar magnet and an electromagnet.

Solution:

Following are the difference between a bar magnet and an electromagnet:

## What is Electromagnetic Induction?

Assume you go cashless when shopping and your parents utilize credit cards. The card is always scanned or swiped by the shopkeeper. The shopkeeper does not photograph or touch the card. However, he swipes/scans it. How does this swiping of the card remove money? This is due to a phenomenon known as ‘Electromagnetic Induction.’

Is it possible for moving things to generate electric currents? How can you tell whether there’s a connection between electricity and magnetism? Consider what life would be like if there were no computers, phones, or electricity. Faraday’s experiments resulted in the development of generators and transformers.

The induction of an electromotive force by the passage of a conductor through a magnetic field or by a change in magnetic flux in a magnetic field is known as electromagnetic induction.

This happens when a conductor is placed in a moving magnetic field or when it moves in a fixed magnetic field.

Michael Faraday discovered this electromagnetic induction rule. He put up a leading wire similar to the diagram above, which he linked to a device that measured the voltage across the circuit. The voltage in the circuit is measured when a bar magnet passes through the device. The significance of this is that it is a method of creating electrical energy in a circuit by employing magnetic fields rather than batteries. The principle of electromagnetic induction is used by devices such as generators, transformers, and motors.

## Faraday law of Electromagnetic Induction

Faraday gave two laws of electromagnetic induction that are called the Faraday law of Electromagnetic Induction that are,

• Faraday’s First Law of Electromagnetic Induction
• Faraday’s Second Law of Electromagnetic Induction

Now let’s learn about these laws in detail.

### Faraday’s First Law of Electromagnetic Induction

When a conductor is put in a changing magnetic field, an induced emf is produced, and if the conductor used is a closed conductor then, an induced current flows through it.

### Faraday’s Second Law of Electromagnetic Induction

The magnitude of the induced EMF is equal to the flux change rate.

Faraday discovered that the induced emf in the coil depends on the various factor that includes,

• Number of Turns in the Coils: The induced voltage is proportional to the number of turns/coils. The more turns there are, the more voltage is created.
• Changing Magnetic Field: The induced voltage is affected by changes in the magnetic field. This can be accomplished by rotating the magnetic field around the conductor or by rotating the conductor inside the magnetic field.

Therefore, Faraday’s law of electromagnetic induction, states that

“The amount of voltage generated in a coil is proportionate to the changing magnetic field and the number of turns of the coil.”

## Lenz’s law of Electromagnetic Induction

Lenz’s Law states that when an emf induces according to Faraday’s law, the polarity (direction) of that induced emf opposes the cause of its creation.

According to Lenz’s law,

E = – N (dϕ ⁄ dt)

where,
E is the EMF produced
N is the number of tunrs of the coil
Negative Sign indicates that the induced emf opposes the cause of its production.

## Eddy Currents

Current loops induced in a conductor when placed in a changing magnetic field are called eddy currents. Eddy currents create a magnetic field that opposes the original magnetic field, which is similar to Lenz’s law. These currents are also called Foucault’s currents. Eddy currents have very useful applications such as metal detectors, electromagnetic braking, induction heating, etc.

Various applications of the Eddy Currents are,

Brakes of Trains: Breaking metal wheels on trains run on metallic tracks and when the brakes are applied, the trains’ metal wheels are exposed to a magnetic field, which induces eddy currents in the wheels. As a result of the magnetic interaction between the applied magnetic field and the eddy currents created in the wheels with friction-based braking, the trains slow down.

Induction Furnaces: The high temperature in the furnaces is prepared using the concept of eddy current.

## Applications of Electromagnetic Induction

Some applications of Electromagnetic Induction are as follows:

• Electromagnetic induction in AC generator
• Electrical Transformers
• Magnetic Flow Meter

### Electromagnetic induction in AC generator

The production of alternating current is one of the most important applications of electromagnetic induction.

More advanced equipment is the AC generator with a 100 MV output capacity. The effective area of the loop, when the coil spins in a magnetic field B, equals A cos θ, where θ is the angle between A and B. The principle of operation of a basic ac generator is this way of creating a flux change. The axis of the rotating coil is perpendicular to the magnetic field direction. The magnetic flux across the coil changes as the coil rotates, causing an emf to induct in the coil.

### Electrical Transformers

An electrical transformer is another major use of electromagnetic induction. A transformer is a device that uses a magnetic field to convert ac electric power from one voltage level to another. The voltage in the primary of a step-down transformer is higher than the voltage in the secondary. A step-up transformer is one in which the secondary voltage has additional turns. To increase the voltage to 100 kV, power providers employ a step transformer, which decreases current and reduces power loss in transmission lines. Household circuits, on the other hand, employ step-down transformers to reduce the voltage to 120 or 240 V.

### Magnetic Flow Meter

Magnetic Flow Meter or Electromagnetic Flow Meter is the device used to measure the velocity or volumetric flow of fluids and uses the principle of electromagnetic induction to do so. Magmeter (commonly used term for Magnetic Flow Meter) can only measure the flow of conductive fluids.

## Solved Examples on Electromagnetic Induction

Example 1: When a bar magnet is placed near to the circular coil having 50 turns, the magnetic field density changes at a rate of 0.10 T ⁄ s. Find the emf induced in the coil.

Solution:

Number of turns, N = 50 turns

Rate of change of magnetic flux, dϕ ⁄ dt = 0.10 T ⁄ s

E = – N (dϕ ⁄ dt)

⇒ E = – 50 × 0.10 V

⇒ E = – 5 V

Hence, the emf induced in the coil is 5 V.

Example 2: A loop of wire is placed in a magnetic field and the magnetic flux through the loop is increasing at a rate of 0.02 T·m²/s. if the resistance of the loop of wire is 5 ohms then what is the induced current in the loop?

Solution:

For a loop of wire, N=1, and the rate of flux increase is 0.02 Tm2/s i.e., dϕ ⁄ dt = 0.02 Tm2/s

resistance of loop of wire is 5 ohm,

According to Lenz’s Law, E = -N(dϕ ⁄ dt)

E = -1×(0.02) = 0.02 Volts

We know Ohm’s Law  states, V = IR

⇒ I = V/R = 0.02/5 = 0.004 Ampere = 4 Mili Ampere

Thus, the Induced current in the wire loop is 4 mili ampere.

## FAQs on Electromagnetic Induction

### Q1: What is Electromagnetic Induction?

Electromagnetic Induction is the induction of an electromotive force by the motion of a conductor through a magnetic field or by a change in magnetic flux in a magnetic field.

### Q2: What is Faraday’s Law of Electromagnetic Induction?

Faraday’s law of electromagnetic induction, states that the amount of voltage generated in a coil is proportionate to the number of turns and the changing magnetic field of the coil.

### Q3: What is Lenz’s Law?

According to Lenz’s law, the induced emf opposes the cause of its production,i.e., E = – N (dϕ ⁄ dt). The negative sign indicates that the induced emf opposes the cause of its production.