NCERT solutions Magnetic Effects of Electric Current class 10

 

Magnetic Effects of Electric Current

 In this chapter, you will learn about the following topics:

• Magnetic field and field lines: You will learn about the concept of magnetic fields and magnetic field lines, how they are represented, and how to draw them.

• Magnetic field due to a current-carrying conductor: You will learn about the right-hand thumb rule to find the direction of the magnetic field around a current-carrying conductor and how to calculate the strength of the magnetic field.

• Magnetic field due to a current through a straight conductor: You will learn about the magnetic field due to a current through a straight conductor and how it varies with distance from the conductor.

• Magnetic field due to a current through a circular loop: You will learn about the magnetic field due to a current through a circular loop and how it varies with distance from the center of the loop.

• Solenoid and its magnetic field: You will learn about solenoids, how they produce a strong magnetic field, and how to calculate the strength of the magnetic field.

• Electromagnetic induction: You will learn about the concept of electromagnetic induction, Faraday's laws of electromagnetic induction, and Lenz's law.

• AC generator: You will learn about the working principle of an AC generator, its construction, and the role of slip rings and brushes.

• DC motor: You will learn about the working principle of a DC motor, its construction, and the role of the commutator.

• Electric motor: You will learn about the different components of an electric motor and how they work together to produce rotational motion.

Magnetic fields and magnetic field lines, how they are represented, and how to draw them

Magnetic fields are a region of space around a magnet or a moving charged particle in which a magnetic force can be detected. They are typically represented by drawing magnetic field lines, which are imaginary lines that show the direction and strength of the magnetic field.

Magnetic field lines are drawn such that the tangent to the line at any point gives the direction of the magnetic field at that point. The direction of the magnetic field is defined as the direction in which the north pole of a magnet would be pulled if placed in the field. Therefore, magnetic field lines always point from the north pole of a magnet to the south pole.

To draw magnetic field lines, you can use the following steps:

• Identify the poles of the magnet or the direction of the moving charged particle.

• Place a compass near the magnet or the charged particle to determine the direction of the magnetic field at various points around it.

• Draw a line tangent to the compass needle at each point to represent the direction of the magnetic field at that point.

• The spacing of the lines can be used to indicate the strength of the magnetic field, with lines closer together indicating a stronger magnetic field.

• The field lines should always form closed loops, as magnetic monopoles (isolated north or south poles) do not exist.

• The field lines should never cross each other, as this would indicate a contradiction in the direction of the magnetic field at that point.

• The overall shape of the field lines will depend on the shape of the magnet or the path of the charged particle.

• By drawing magnetic field lines, we can visualize and better understand the behavior of magnetic fields, such as how they interact with other magnetic fields or with charged particles.

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Magnetic field due to a current-carrying conductor: 

The magnetic field around a current-carrying conductor can be determined using the right-hand rule. If you wrap your right-hand around the conductor with your fingers pointing in the direction of the current, your thumb will point in the direction of the magnetic field lines.

The strength of the magnetic field is directly proportional to the current flowing through the conductor, and inversely proportional to the distance from the conductor. The formula for the magnetic field around a long straight conductor is given by:

B = (μ₀/4π) * (I / r)

where B is the magnetic field in teslas (T), I is the current in amperes (A), r is the distance from the conductor in meters, and μ₀ is the permeability of free space, which is approximately equal to 4π x 10^-7 T*m/A.

For a solenoid or a coil with N turns of wire, the magnetic field can be calculated using the formula:

B = (μ₀/4π) * (N * I / l)

where l is the length of the solenoid or coil.

It's important to note that the magnetic field around a current-carrying conductor is a vector quantity, which means that it has both magnitude and direction. The direction of the magnetic field lines depends on the direction of the current, and the magnetic field lines form closed loops around the conductor.

Magnetic field due to a current through a straight conductor 

The magnetic field generated by a current-carrying straight conductor can be calculated using Ampere's law. According to Ampere's law, the magnetic field at a distance r from a long, straight conductor carrying a current I is given by:

B = μ₀I/2πr

Where μ₀ is the permeability of free space, which has a value of 4π x 10^-7 N/A^2.

The above equation shows that the magnetic field strength B decreases with distance r from the conductor. Specifically, the magnetic field varies inversely with the distance r from the conductor, so as r increases, B decreases.

The direction of the magnetic field can be determined using the right-hand rule. If you wrap your right hand around the conductor with your thumb pointing in the direction of the current, your fingers will curl in the direction of the magnetic field lines.

In summary, the magnetic field due to a current through a straight conductor decreases with distance from the conductor and its direction can be determined using the right-hand rule.

Magnetic field due to a current through a circular loop how it varies with distance from the center of the loop.

The magnetic field due to a current through a circular loop varies with distance from the center of the loop according to the inverse square law. This means that the magnetic field strength decreases as the distance from the center of the loop increases.

Specifically, the magnetic field strength at a point on the axis of the loop (perpendicular to the plane of the loop) a distance r from the center of the loop is given by:

B = (μ₀I/2R) * (R²/(R² + r²)^(3/2))

Where B is the magnetic field strength, I is the current in the loop, R is the radius of the loop, r is the distance from the center of the loop to the point where the field is being measured, and μ₀ is the permeability of free space.

This formula shows that the magnetic field strength is directly proportional to the current and the radius of the loop, and inversely proportional to the distance from the center of the loop. The closer the point is to the center of the loop, the stronger the magnetic field will be.

Solenoid and its magnetic field how they produce a strong magnetic field, and how to calculate the strength of the magnetic field.

A solenoid is a long coil of wire that is used to produce a strong magnetic field. When a current flows through the wire, a magnetic field is generated around the coil. The strength of the magnetic field depends on the number of turns in the coil, the current flowing through the wire, and the physical properties of the core material (if one is present).

The magnetic field produced by a solenoid is similar to that produced by a bar magnet, with the field lines running from one end of the coil to the other. However, unlike a bar magnet, the magnetic field inside a solenoid is very uniform, meaning that it has the same strength and direction at all points within the coil.

The strength of the magnetic field produced by a solenoid can be calculated using the formula:

B = μnI

where B is the magnetic field strength (in Tesla), μ is the permeability of the material (in Henrys per meter), n is the number of turns per unit length of the coil (in turns per meter), and I is the current flowing through the wire (in Amperes).

If the solenoid has a core material, then the strength of the magnetic field can be increased by choosing a material with a high permeability. This is because the permeability of the material determines how easily the magnetic field can pass through it.

In summary, a solenoid produces a strong magnetic field when a current flows through its coil. The strength of the magnetic field depends on the number of turns in the coil, the current flowing through the wire, and the physical properties of the core material. The magnetic field can be calculated using the formula B = μnI.

Electromagnetic Induction and Faraday laws of electromagnetic induction, and Lenz's law.

Electromagnetic induction is the process by which a changing magnetic field induces an electric current in a conductor. It is based on two fundamental laws, known as Faraday's laws of electromagnetic induction, and a complementary law known as Lenz's law.

Faraday's first law states that when a conductor is placed in a changing magnetic field, an electromotive force (EMF) is induced in the conductor. The magnitude of the induced EMF is proportional to the rate of change of the magnetic field with respect to time, and is given by the equation:

EMF = -dΦ/dt

where EMF is the induced electromotive force (in volts), Φ is the magnetic flux (in webers), and t is time (in seconds). The negative sign in the equation indicates that the direction of the induced EMF is such that it opposes the change in the magnetic field.

Faraday's second law states that the magnitude of the EMF induced in a closed loop is equal to the rate of change of the magnetic flux through the loop. The equation for this law is:

EMF = -dΦ/dt

where EMF is the induced electromotive force (in volts), Φ is the magnetic flux (in webers), and t is time (in seconds).

Lenz's law is a complementary law to Faraday's laws of electromagnetic induction, which states that the direction of the induced current in a conductor is such that it opposes the change in the magnetic field that produced it. This means that when a magnetic field is increasing, the induced current will flow in a direction such that it produces a magnetic field that opposes the increase in the original magnetic field.

Similarly, when a magnetic field is decreasing, the induced current will flow in a direction such that it produces a magnetic field that opposes the decrease in the original magnetic field. Lenz's law is based on the conservation of energy and the principle of least action, and is a fundamental law of electromagnetism.

In summary, Faraday's laws of electromagnetic induction state that a changing magnetic field induces an electromotive force in a conductor, and the magnitude of the induced EMF is proportional to the rate of change of the magnetic field. Lenz's law states that the direction of the induced current is such that it opposes the change in the magnetic field that produced it.

AC generator and working principle of an AC generator, its construction, and the role of slip rings and brushes.

• An AC generator, also known as an alternator, is a device that converts mechanical energy into electrical energy. It works on the principle of electromagnetic induction, which states that a changing magnetic field induces an electromotive force (EMF) in a conductor.

• The construction of an AC generator includes a stationary component, known as the stator, and a rotating component, known as the rotor. The stator contains a set of stationary coils of wire, arranged around the circumference of the generator, while the rotor contains a set of rotating magnets or coils, mounted on a shaft. As the rotor rotates, it creates a changing magnetic field that induces an EMF in the stationary coils of the stator.

• The role of slip rings and brushes in an AC generator is to transfer the electrical energy from the rotating component (the rotor) to the stationary component (the stator). The slip rings are conductive rings that are mounted on the shaft of the rotor and rotate with it. The brushes are stationary contacts that are pressed against the slip rings, allowing electrical current to flow from the rotor to the stator.

• The slip rings and brushes provide a continuous electrical connection between the rotating and stationary components of the generator, allowing the induced EMF in the stator to be collected and transmitted to an external load, such as a light bulb or an electric motor.

DC Motor and  working principle of a DC motor, its construction, and the role of the commutator.

• A DC motor, short for direct current motor, is a type of electric motor that converts electrical energy into mechanical energy. It works on the principle of Lorentz's law of electromagnetism, which states that when a current-carrying conductor is placed in a magnetic field, a force is generated on the conductor. This force causes the conductor to move, and in a DC motor, it causes the motor shaft to rotate.

• The construction of a DC motor typically consists of several main components, including a stator, rotor, commutator, brushes, and a power supply. The stator is the stationary part of the motor and contains the magnetic field. The rotor is the rotating part of the motor and is connected to the shaft. The commutator is a cylindrical structure mounted on the rotor, consisting of a set of copper segments separated by insulating material. The brushes are typically made of carbon and are in contact with the commutator segments.

• When a DC voltage is applied to the motor, current flows through the coils of the rotor, creating a magnetic field. This magnetic field interacts with the magnetic field of the stator, generating a force that causes the rotor to rotate. As the rotor rotates, the commutator segments come into contact with the brushes, which transfer current to the coils in the rotor. The commutator segments change the direction of the current flow in the rotor coils, ensuring that the magnetic field in the rotor is always perpendicular to the magnetic field in the stator. This constant change in the direction of the magnetic field in the rotor ensures that the rotor continues to rotate.

• The commutator plays a crucial role in the operation of a DC motor. Its function is to switch the direction of the current in the rotor coils as the rotor rotates. This switching action ensures that the magnetic field in the rotor is always perpendicular to the magnetic field in the stator, allowing the motor to rotate continuously. Without a commutator, the motor would not be able to rotate, as the magnetic field in the rotor would remain fixed in one direction and would not interact with the magnetic field in the stator.

Electric motor and different components of an electric motor and how they work together to produce rotational motion

An electric motor is a device that converts electrical energy into mechanical energy. It works on the principle of electromagnetic induction, which states that when a conductor is placed in a magnetic field and an electric current is passed through it, a force is generated that causes the conductor to move. In an electric motor, this force is used to produce rotational motion.

There are several main components of an electric motor, including the stator, rotor, commutator, brushes, and power supply. These components work together to produce rotational motion.

Stator: The stator is the stationary part of the motor and contains the magnetic field. It is typically made up of multiple coils of wire wound around a central core. When an electrical current is passed through the coils, a magnetic field is generated.

Rotor: The rotor is the rotating part of the motor and is connected to the shaft. It is typically made up of multiple coils of wire wound around a central core. The rotor is placed inside the magnetic field of the stator and is free to rotate.

Commutator: The commutator is a cylindrical structure mounted on the rotor, consisting of a set of copper segments separated by insulating material. The commutator serves as a switch that allows the electrical current to flow to the coils in the rotor.

Brushes: The brushes are typically made of carbon and are in contact with the commutator segments. The brushes transfer current to the coils in the rotor as the commutator rotates, allowing the magnetic field in the rotor to interact with the magnetic field in the stator.

Power supply: The power supply provides the electrical energy that is converted into mechanical energy by the motor. In a DC motor, the power supply is typically a battery or a DC power supply.

• When a DC voltage is applied to the motor, current flows through the coils of the stator, creating a magnetic field. The magnetic field in the stator interacts with the magnetic field in the rotor, generating a force that causes the rotor to rotate. As the rotor rotates, the commutator segments come into contact with the brushes, which transfer current to the coils in the rotor. The commutator segments change the direction of the current flow in the rotor coils, ensuring that the magnetic field in the rotor is always perpendicular to the magnetic field in the stator. This constant change in the direction of the magnetic field in the rotor ensures that the rotor continues to rotate.

In summary, the stator provides the magnetic field, the rotor rotates inside the magnetic field, the commutator and brushes transfer current to the rotor coils, and the power supply provides the electrical energy that is converted into mechanical energy. All these components work together to produce rotational motion in an electric motor.