Magnetism and Matter — Class 12 Physics Notes

Topics covered in Magnetism and Matter

1. 1.Introduction of Magnetism And Matter

   Short Answer

   Magnetism and Matter deals with the properties of magnets, the magnetic field, and how various materials react to magnetic fields. It's used in everyday technology like compasses, motors, and data storage devices.

   Long Answer

   Introduction

   Magnetism is a force experienced by materials that respond to magnetic fields. This branch of physics involves studying magnetic fields, which are invisible lines that show the direction of magnetic forces.

   Key Concepts

   1. Magnetic Field: It surrounds a magnet and represents the area where magnetic forces can be observed. It's strongest at the poles of the magnet.
   2. Magnetic Poles: Every magnet has two poles, North and South. Opposite poles attract, and like poles repel each other.
   3. Magnetic Materials: Materials that can be magnetized or attracted by a magnet. Examples include iron, nickel, and cobalt.
   4. Earth’s Magnetism: Earth acts like a giant magnet with magnetic poles near the geographic poles. This is why compasses point north.

   Real-Life Examples

   • Compasses use Earth's magnetic field to help navigate by pointing towards the magnetic North Pole.
   • Electric Motors work on the principle of magnetism where electric current through coils generates magnetic fields, driving the motor.
   • Data Storage: Hard drives and credit cards use magnetic materials to store data.

   Applications in Careers and Industries

   • Engineering: Designing motors, generators, and magnetic sensors.
   • Environmental Science: Studying Earth's magnetic field changes to understand plate tectonics.
   • Data Storage Technology: Creating and improving storage devices like hard drives and memory cards.

   Activity to Understand Magnetism

   Try this simple activity: Take a small magnet and some paper clips. Scatter the clips on a table and slowly bring the magnet close to them. Notice how the clips align themselves along the magnetic field lines of the magnet. This demonstrates how magnetic forces work.

2. 2.Bar Magnet

   Short Answer

   A bar magnet is a rectangular piece of object, usually made of iron, steel, or any magnetic material, which exhibits magnetic properties such as attracting iron pieces. The magnetic field lines of a bar magnet emerge from the north pole and merge at the south pole, showing the direction of the magnetic field around the magnet. A bar magnet can be thought of as an equivalent solenoid (a coil of wire) with a current flowing through it, creating a similar magnetic field. When a magnetic dipole (like a bar magnet) is placed in a uniform magnetic field, it experiences a torque that aligns it with the magnetic field.

   Long Answer

   The Bar Magnet and Its Magnetic Field Lines

   1. Concept: A bar magnet is a simple rectangular object that creates a magnetic field around itself. This field is visualized by magnetic field lines.

   2. Magnetic Field Lines: These lines start from the magnet's north pole and end at its south pole outside the magnet, while inside the magnet, they move from the south pole to the north pole, forming closed loops. These lines are a way to represent the direction and strength of the magnetic field. Closer lines mean a stronger magnetic field.

   Activity: Use a compass and a bar magnet. Place the compass near the magnet and watch how the compass needle aligns with the magnet's magnetic field lines. Move the compass around the magnet to see how the direction of the magnetic field changes.

   Real-Life Example: The Earth itself acts like a giant bar magnet with magnetic poles near its geographic poles. This is why compasses point north-south.

   3. Formula for Magnetic Field due to a Bar Magnet at a Point: The magnetic field due to a bar magnet at a point on its axial line is given by =0423B=4πμ0​​r32m​, where B is the magnetic field, 0μ0​ is the permeability of free space, m is the magnetic moment of the bar magnet, and r is the distance from the center of the magnet to the point.

   Bar Magnet as an Equivalent Solenoid

   1. Concept: A solenoid is a coil of wire that produces a magnetic field when an electric current passes through it. A bar magnet can be considered equivalent to a solenoid with a current flowing through it.

   2. Derivation: The magnetic field inside a long solenoid is given by =0B=μ0​nI, where n is the number of turns per unit length, and I is the current. By adjusting the current and the number of turns, a solenoid can be made to mimic the magnetic field of a bar magnet.

   Real-Life Use: This concept is used in electromagnets and motors where controlling the magnetic field is required.

   The Dipole in a Uniform Magnetic Field

   1. Concept: A magnetic dipole, like a small bar magnet, when placed in a uniform magnetic field, experiences a torque that tries to align it with the field.

   2. Formula and Derivation: The torque (τ) experienced by the dipole is given by =sin⁡τ=mBsinθ, where m is the magnetic moment of the dipole, B is the magnetic field strength, and θ is the angle between the magnetic moment and the magnetic field. This formula is derived from the principle that the potential energy of a magnetic dipole in a magnetic field is =−cos⁡U=−mBcosθ, and torque is the rate of change of this potential energy with respect to θ.

   Real-Life Application: This principle is used in magnetic compasses and in various scientific instruments to measure the strength of magnetic fields.

3. 3.Magnetism And Gauss’s Law

   Short Answer

   The diagram shows a small area (ΔΔS) with a magnetic field (B) passing through it. The angle θ is the angle between the normal to the surface (^n^) and the magnetic field. Gauss's Law for magnetism states that the net magnetic flux through a closed surface is zero, implying that magnetic monopoles do not exist.

   Long Answer

   Explanation with the Diagram:

   1. Magnetic Field (B): Represented by the lines, this is the magnetic field through which the area element (ΔΔS) is placed.

   2. Area Element (ΔΔS): This is a tiny, flat surface through which the magnetic field lines are passing.

   3. Normal Vector (^n^): This is a vector perpendicular to the area element.

   4. Angle θ: This is the angle between the magnetic field and the normal to the area element.

   Gauss's Law for Magnetism Formula:

   Gauss's Law for magnetism can be expressed mathematically as: ∮⋅=0∮S​B⋅dA=0 where B is the magnetic field, dA is the differential area vector (with direction normal to the surface), and the integral is evaluated over a closed surface S.

   Derivation and Mathematical Expression:

   The derivation of Gauss's Law for magnetism is based on experimental observations that magnetic monopoles do not exist. The magnetic flux (ΦΦB​) through a surface is defined as: Φ=∫⋅ΦB​=∫S​B⋅dA For a closed surface, the law dictates that the number of field lines entering and leaving the surface must be equal, hence the net flux is zero.

   Numerical Example:

   Let's say we want to calculate the magnetic flux through a flat square surface of side l placed in a uniform magnetic field B that makes an angle θ with the normal to the surface.

   The area of the surface =2A=l2, and the magnetic flux ΦΦB​ would be: Φ=⋅⋅cos⁡ΦB​=B⋅A⋅cos(θ) Φ=⋅2⋅cos⁡ΦB​=B⋅l2⋅cos(θ)

   If =2B=2 Tesla, =0.1l=0.1 m, and =30∘θ=30∘: Φ=2⋅(0.1)2⋅cos⁡(30∘)ΦB​=2⋅(0.1)2⋅cos(30∘) Φ=0.02⋅3/2ΦB​=0.02⋅3​/2 Φ=0.01732ΦB​=0.01732 Weber (Wb)

   This is the magnetic flux through that surface, but remember, for a closed surface the total flux would be zero according to Gauss's Law.

4. 4.Magnetization & Magnetic Intensity

   Short Answer

   Magnetization refers to the magnetic moment per unit volume of a material and is denoted by M. Magnetic intensity, also known as magnetic field intensity or magnetic field strength, is denoted by H. It represents the concentration of magnetic field lines in a material or space.

   Long Answer

   1. Magnetization (M):

   Magnetization is a measure of the degree to which a material can be magnetized. It is a vector quantity that represents the density of magnetic dipole moments in a magnetic material. It's induced by an external magnetic field and can be permanent in ferromagnetic materials.

   Formula: =Total Magnetic MomentVolumeM=VolumeTotal Magnetic Moment​

   2. Magnetic Intensity (H):

   Magnetic intensity is a vector field that represents how strong and in what direction a magnetic field will affect ferromagnetic materials within it. It's related to the magnetizing force that causes magnetization in a material.

   Formula: =0−H=μ0​B​−M where B is the magnetic flux density, and 0μ0​ is the permeability of free space.

   3. Relationship between M and H:

   In a material, the magnetization M is proportional to the applied magnetic intensity H up to a point for ferromagnetic materials. The proportionality constant is known as magnetic susceptibility (χm​).

   Formula: =M=χm​H

   Magnetization (M) is explained as the net magnetic moment per unit volume of a material. It's a vector quantity that represents how much a material will be magnetized in response to an applied magnetic field. The formula given is:

   =netM=Vmnet​​

   where netmnet​ is the net magnetic moment and V is the volume.

   Magnetic Intensity (H), also known as magnetic field strength, is a vector field that is defined by the formula:

   =0−H=μ0​B​−M

   where B is the magnetic flux density, 0μ0​ is the permeability of free space, and M is the magnetization. H essentially quantifies the magnetic field produced by both free currents and the material's magnetization.

   When a material with a non-zero magnetization is placed inside a solenoid, the net magnetic field (B) inside the solenoid is the vector sum of the field due to the solenoid (0B0​) and the field due to the material's magnetization (Bm​), expressed as:

   =0+B=B0​+Bm​

   where Bm​ is related to the magnetization M by:

   =0Bm​=μ0​M

   In the case where the internal magnetic field is modified by a material inside the solenoid, the relationship can be expressed as:

   =0(+)B=μ0​(H+M)

   Here, 0μ0​ is the magnetic permeability of free space.

   The concept of magnetic susceptibility (χ) is introduced, which is a measure of how much a material can be magnetized by an external field. It's given by:

   =M=χH

   Finally, they define the relative permeability (μr​), which is a dimensionless quantity given by:

   =1+μr​=1+χ

   And therefore, the relationship between B, H, and M in a material is summarized as:

   =0B=μ0​μr​H

   These formulas and concepts are fundamental in understanding how materials respond to magnetic fields and are crucial for applications in electromagnetism, including the design of electrical devices, magnetic storage media, and medical imaging systems.

   Real-Life Application:

   Understanding M and H is essential in designing and manufacturing magnetic devices such as hard drives, MRI machines, and electric motors, where the manipulation of magnetic properties is crucial.

5. 5.Magnetic Properties of Material

   Short Answer

   Magnetic properties of materials describe how materials respond to an external magnetic field. They are classified into three types based on their magnetic susceptibility (c):

   1. Diamagnetic materials have a negative susceptibility, meaning they are repelled by magnetic fields.
   2. Paramagnetic materials have a positive but small susceptibility, meaning they are weakly attracted to magnetic fields.
   3. Ferromagnetic materials have a large and positive susceptibility, meaning they are strongly attracted to magnetic fields and can become permanently magnetized.

   These properties are crucial in various applications, like in MRI machines (using diamagnetic properties), in storing information in hard drives (ferromagnetism), and in sensors and actuators (paramagnetism).

   Long Answer

   1. Diamagnetism

   Diamagnetic materials are characterized by their negative magnetic susceptibility. This means that when an external magnetic field is applied, they create an induced magnetic field in the opposite direction, leading to a repulsive effect. This happens because the orbiting electrons in the material adjust to cancel out the applied field.

   Real-life Example: Water and graphite are diamagnetic. When you place them in a magnetic field, they will weakly repel the magnetic field.

   Activity: Place a small piece of graphite on water and bring a strong magnet close to it. You will notice the graphite slightly repels away from the magnet.

   Use in Life: Diamagnetic materials are used in magnetic levitation, where objects are made to float in the air without any support, other than magnetic fields.

   Career or Industry: Research and development in advanced materials and technologies, especially in designing systems for magnetic levitation transport or in medical technologies like MRI machines.

   2. Paramagnetism

   Paramagnetic materials have a small but positive susceptibility to magnetic fields. They are attracted by magnetic fields, but the effect is weak and only noticeable when the external field is strong. This attraction is due to unpaired electrons in the material aligning with the external magnetic field.

   Real-life Example: Aluminum and oxygen are paramagnetic. They are attracted to magnetic fields but do not retain magnetization once the field is removed.

   Activity: Hang a small aluminum rod using a thread and bring a strong magnet close to it. You will notice the rod aligning itself with the direction of the magnetic field.

   Use in Life: Paramagnetic materials are used in various sensors and as contrast agents in MRI scans to enhance the quality of the image.

   Career or Industry: Healthcare for MRI imaging, and engineering for designing sensors and actuators.

   3. Ferromagnetism

   Ferromagnetic materials have a large and positive susceptibility to magnetic fields. They are strongly attracted to magnetic fields and can retain their magnetization even after the external field is removed, a property known as hysteresis.

   Real-life Example: Iron, cobalt, and nickel are ferromagnetic materials. They can become permanently magnetized.

   Activity: Stroke a piece of iron with a strong magnet several times in one direction. The iron piece becomes magnetized and can attract small iron filings or pins.

   Use in Life: Ferromagnetic materials are fundamental in making permanent magnets, used in motors, electrical generators, hard drives for data storage, and in various electronic devices.

   Career or Industry: Electronics, automotive, data storage, and energy sectors rely heavily on ferromagnetic materials for developing products and technologies.