## Introduction: moving charges and magnetism

In physics, magnetism is a force that arises from the motion of electric charges. Every time an electric charge moves, it creates a magnetic field around it. This is because the movement of electric charges is what produces magnetism.

There are two types of magnetism: diamagnetism and paramagnetism. Diamagnetism is the property of a substance to become magnetized in the presence of an external magnetic field. Paramagnetism is the property of a substance to become magnetized in the presence of an external magnetic field, but to a lesser extent than diamagnetic materials.

Magnetic fields are created by electric currents. When an electric current flows through a wire, it creates a magnetic field around the wire. The direction of the magnetic field is determined by the direction of the electric current.

The strength of a magnetic field is measured in units called tesla (T). The Earth’s magnetic field is about 0.00005 T. In comparison, the magnetic field of a typical refrigerator magnet is about 0.0001 T.

## Some Laws of Electromagnetism

There are several laws that describe the behavior of magnetic fields. The first is the Biot-Savart Law, which describes how the magnetic field varies with distance from a current-carrying wire. The second is the Ampere’s Law, which describes the relationship between the current and the magnetic field it creates. The third is the Faraday’s Law of Electromagnetic Induction, which describes how a changing magnetic field can induce an electric current in a conductor.

**1 . The Biot-Savart Law:** This law describes the magnetic field created by a current-carrying wire. It states that the magnetic field at a point in space is directly proportional to the current flowing through the wire, and inversely proportional to the distance from the wire.

It is expressed as:

B = (μo / 4π) * I * (dl x r) / r^2

where B is the magnetic field at a point in space, μo is the permeability of free space, I is the current flowing through the wire, dl is a small element of the wire, and r is the distance from the wire to the point in space.

The direction of the magnetic field is perpendicular to the plane formed by the wire and the point in space, and is given by the right-hand rule.

**2 . Faraday’s Law of Electromagnetic Induction:** This law describes how a changing magnetic field can induce an electric current in a conductor. It states that the electromotive force (EMF) induced in a conductor is equal to the rate of change of the magnetic flux through the conductor.

It is expressed as:

EMF = -dφ/dt

where EMF is the electromotive force, dφ is the change in magnetic flux, and dt is the change in time.

The magnetic flux is the product of the magnetic field and the surface area of the conductor. It is expressed as:

φ = B * A

where φ is the magnetic flux, B is the magnetic field, and A is the surface area of the conductor.

**3 . Ampere’s Law:** Ampere Law is a fundamental law of electromagnetism that relates the magnetic field around a conductor to the electric current flowing through the conductor. It states that the integral of the magnetic field around a closed path is equal to the current passing through the path, multiplied by a constant called the permeability of free space (μo).

Mathematically, Ampere’s Law is expressed as:

∫B.ds = μo * I

where ∫B.ds is the integral of the magnetic field around the closed path, μo is the permeability of free space, and I is the current passing through the path.

Ampere’s Law is a useful tool for calculating the magnetic field due to a current-carrying conductor. It can be used to calculate the magnetic field due to a straight wire, a loop of current, or a more complex current distribution.

Ampere’s Law is based on the assumption that the current is uniformly distributed throughout the conductor. It is also based on the assumption that the magnetic field is uniform around the conductor. These assumptions may not always be valid, especially for complex current distributions or conductors with a non-uniform cross-section. In these cases, Ampere’s Law may need to be modified or extended using techniques such as Ampere’s Circuit Law.

**4 . Lenz’s Law:** Lenz Law is a fundamental law of electromagnetism that relates the direction of an induced current in a conductor to the change in magnetic flux that caused it. It states that the induced current will always act to oppose the change in magnetic flux that caused it.

Mathematically, Lenz’s Law is expressed as:

I = -dφ/dt

where I is the induced current, dφ is the change in magnetic flux, and dt is the change in time.

Lenz’s Law is based on the principle of conservation of energy. It states that the induced current will act to reduce or eliminate the change in the magnetic field that caused it, in order to minimize the energy required to maintain the field.

Lenz’s Law can be used to predict the direction of an induced current in a conductor. To do this, the direction of the induced current is determined by the right-hand rule, which states that the direction of the current is given by the thumb of the right hand, when the fingers are pointed in the direction of the change in magnetic flux.

**5 . Lorentz’s force law: **The Lorentz force law is a fundamental law of electromagnetism that relates the force acting on a charged particle to the electric and magnetic fields acting on the particle. It states that the force acting on a charged particle is equal to the product of the particle’s charge, the electric field acting on the particle, and the particle’s velocity, plus the product of the particle’s charge, the magnetic field acting on the particle, and the cross product of the particle’s velocity and the magnetic field.

Mathematically, the Lorentz force law is expressed as:

F = q(E + v x B)

where F is the force acting on the charged particle, q is the charge of the particle, E is the electric field, v is the velocity of the particle, and B is the magnetic field.

The Lorentz force law is a useful tool for calculating the force acting on a charged particle in an electric and magnetic field. It is used in a variety of applications, including the design of particle accelerators and the study of the motion of charged particles in magnetic fields.

## Moving charges and Magnetism Handwritten Notes

**👉 Magnetic Field Lines: **Magnetic field lines are used to represent the strength and direction of a magnetic field. The lines always point in the direction that a north pole of a magnet would move if placed in the field. The lines are closer together in areas where the field is stronger, and farther apart in areas where the field is weaker.

**👉 Magnetic Forces on Moving Charges:** A moving charge experiences a force in a magnetic field due to its interaction with the magnetic field. The force is given by the Lorentz force law, which states that the force on a moving charge is equal to the charge times the velocity of the charge, times the cross product of the magnetic field and the unit vector in the direction of the velocity. The direction of the force is given by the right-hand rule.

**👉 Magnetic Forces on Current-Carrying Wires: **A current-carrying wire experiences a force in a magnetic field due to the interaction of the magnetic field with the moving charges in the wire. The force is given by the force per unit length, which is equal to the current in the wire times the cross product of the magnetic field and the unit vector in the direction of the wire. The direction of the force is given by the right-hand rule.

**👉** **Electromagnets**: An electromagnet is a type of magnet that is created by passing an electric current through a wire. The strength of the electromagnet can be controlled by changing the amount of current flowing through the wire. Electromagnets are commonly used in a variety of applications, including doorbells, motors, and MRI machines.

**👉** **Magnetic Dipoles**: A magnetic dipole is a combination of two magnetic poles, a north pole and a south pole, separated by some distance. The strength of a magnetic dipole is measured by its magnetic moment, which is equal to the product of the strength of one of the poles and the distance between the poles. Magnetic dipoles can be created by electric currents, and can also be found in naturally occurring materials such as magnets.

**👉** **Magnetic Field Due to a Loop of Current**: The magnetic field due to a loop of current can be calculated using the Biot-Savart Law. The field at a point a distance r from the center of the loop is given by:

B = (μo / 4π) * I * (2πr / r)

where B is the magnetic field at the point, μo is the permeability of free space, I is the current flowing through the loop, and r is the distance from the point to the center of the loop.

**👉** **Magnetic Field Due to a Straight Wire**: The magnetic field due to a straight wire can be calculated using the Biot-Savart Law. The field at a point a distance r from the wire is given by:

B = (μo / 4π) * I / r

where B is the magnetic field at the point, μo is the permeability of free space, I is the current flowing through the wire, and r is the distance from the point to the wire.

**👉** **Magnetic Field Due to a Solenoid**: A solenoid is a long coil of wire that creates a strong magnetic field when an electric current flows through it. The field inside a solenoid is uniform and directed along the axis of the solenoid. The field can be calculated using the Biot-Savart Law and the equation for the field due to a loop of current.

**👉** **Torque on a Current Loop**: A current loop placed in a magnetic field will experience a torque, which is a force that tends to rotate the loop about its axis. The torque is given by the product of the magnetic moment of the loop, the magnetic field, and the sine of the angle between the magnetic moment and the field.

**👉** **Magnetic Field Due to a Bar Magnet**: The magnetic field due to a bar magnet can be calculated using the Biot-Savart Law. The field at a point a distance r from the center of the magnet is given by:

B = (μo / 4π) * (2πr / r^3) * m

where B is the magnetic field at the point, μo is the permeability of free space, r is the distance from the point to the center of the magnet, and m is the magnetic moment of the magnet.

**👉** **Magnetic Field Due to a Current Sheet**: A current sheet is a thin layer of current flowing in a plane. The magnetic field due to a current sheet can be calculated using the Biot-Savart Law. The field at a point a distance r from the sheet is given by:

B = (μo / 2) * I / r

where B is the magnetic field at the point, μo is the permeability of free space, I is the current flowing through the sheet, and r is the distance from the point to the sheet.

**👉** **Force on a Current-Carrying Wire in a Magnetic Field:** A current-carrying wire placed in a magnetic field will experience a force due to the interaction of the magnetic field with the moving charges in the wire. The force is given by the product of the current in the wire, the length of the wire, the magnetic field, and the sine of the angle between the wire and the field. The direction of the force is given by the right-hand rule.

**👉** **Magnetic Field Due to a Toroidal Solenoid**: A toroidal solenoid is a solenoid that is shaped like a donut, with a hole in the center. The magnetic field due to a toroidal solenoid can be calculated using the Biot-Savart Law and the equation for the field due to a loop of current.

**👉** **Magnetic Field Due to a Flat Spiral**: A flat spiral is a spiral-shaped conductor with a uniform current flowing through it. The magnetic field due to a flat spiral can be calculated using the Biot-Savart Law and the equation for the field due to a current sheet.

**👉** **Magnetic Field Due to a Spherical Shell**: A spherical shell is a thin, spherical conductor with a uniform current flowing through it. The magnetic field due to a spherical shell can be calculated using the Biot-Savart Law and the equation for the field due to a loop of current.

**👉** **Magnetic Field Due to a Cylindrical Shell**: A cylindrical shell is a thin, cylindrical conductor with a uniform current flowing through it. The magnetic field due to a cylindrical shell can be calculated using the Biot-Savart Law and the equation for the field due to a loop of current.

**👉** **Magnetic Field Due to a Disk**: A disk is a thin, flat conductor with a uniform current flowing through it. The magnetic field due to a disk can be calculated using the Biot-Savart Law and the equation for the field due to a current sheet.

**👉** **Magnetic Field Due to a Ring**: A ring is a thin, circular conductor with a uniform current flowing through it. The magnetic field due to a ring can be calculated using the Biot-Savart Law and the equation for the field due to a loop of current.

**👉** **Induced Electric Fields**: An induced electric field is an electric field that is created by a changing magnetic field. The electric field is perpendicular to the magnetic field and is given by the equation:

E = -dB/dt

where E is the electric field, B is the magnetic field, and dt is the change in time.

**👉** **Transformers**: A transformer is a device that uses electromagnetic induction to convert alternating current (AC) voltage from one value to another. The transformer consists of two coils of wire, a primary coil and a secondary coil, that are magnetically coupled through an iron core. The voltage in the secondary coil is given by the ratio of the number of turns in the primary and secondary coils.

**👉** **Electric Generators**: An electric generator is a device that converts mechanical energy into electrical energy. It consists of a coil of wire that is rotated in a magnetic field, which creates a changing magnetic flux and an induced EMF in the coil. The induced EMF drives a current through a load, which converts the mechanical energy into electrical energy.

**👉** **Electromagnetic Waves**: Electromagnetic waves are waves that are created by the oscillation of electric and magnetic fields. They are a type of radiant energy that travels through empty space at the speed of light. Examples of electromagnetic waves include radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays.

**👉** **Electromagnetic Spectrum**: The electromagnetic spectrum is a range of electromagnetic waves arranged according to their frequency or wavelength. The spectrum is divided into several regions, including radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays. Each region of the spectrum has different properties and applications.

**👉** **Electromagnetic Induction**: Electromagnetic induction is the process by which a changing magnetic field creates an electric field, which in turn drives a current through a conductor. This process is the basis for Faraday’s Law of Electromagnetic Induction and Lenz’s Law.

**👉** **Magnetic Flux Density**: The magnetic flux density is a measure of the strength of a magnetic field. It is defined as the magnetic flux per unit area of a surface. The magnetic flux density is given by the equation:

B = φ / A

where B is the magnetic flux density, φ is the magnetic flux, and A is the surface area.

The unit of magnetic flux density is the tesla (T).

**👉** **Magnetic Permeability**: The magnetic permeability of a material is a measure of its ability to support a magnetic field. It is defined as the ratio of the magnetic flux density to the magnetizing field strength. The magnetic permeability of a material is given by the equation:

μ = B / H

where μ is the magnetic permeability, B is the magnetic flux density, and H is the magnetizing field strength.

The unit of magnetic permeability is the henry per meter (H/m).

**👉** **Magnetic Materials**: Magnetic materials are materials that are capable of being magnetized. There are two types of magnetic materials: ferromagnetic and paramagnetic. Ferromagnetic materials, such as iron, cobalt, and nickel, are materials that are strongly magnetized in the presence of a magnetic field. Paramagnetic materials, such as aluminum and platinum, are materials that are weakly magnetized in the presence of a magnetic field.

**👉** **Ferromagnetism**: Ferromagnetism is the type of magnetism that is observed in ferromagnetic materials. It is a strong type of magnetism that is caused by the alignment of the magnetic moments of the atoms within the material. Ferromagnetic materials are capable of being permanently magnetized and can be used to make magnets.

**👉** **Diamagnetism**: Diamagnetism is the type of magnetism that is observed in all materials. It is a weak type of magnetism that is caused by the movement of the electrons within the material. Diamagnetic materials are not permanently magnetized and are not attracted to magnets.

**👉** **Hysteresis**: Hysteresis is the property of a magnetic material to retain a residual magnetization after the magnetizing field is removed. It is a measure of the energy loss associated with the magnet.

**👉** **Solenoid**: A solenoid is a coil of wire that creates a strong magnetic field when an electric current flows through it. The field inside a solenoid is uniform and directed along the axis of the solenoid. Solenoids are commonly used in a variety of applications, including motors, generators, and electromagnets.

**👉** **Electromagnetic Force**: The electromagnetic force is the force that acts between two charged particles due to their electromagnetic interaction. It is a fundamental force of nature and is one of the four fundamental forces of the universe, along with the strong nuclear force, the weak nuclear force, and the gravitational force.

**👉** **Electromagnetic Energy**: Electromagnetic energy is a type of energy that is associated with the electromagnetic force. It is a form of radiant energy that travels through empty space at the speed of light. Examples of electromagnetic energy include radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays.

**👉** **Electromagnetic Field**: An electromagnetic field is a field of energy that is created by the movement of electric charges. It is composed of both an electric field and a magnetic field. The strength and direction of the field is determined by the movement and distribution of the electric charges.

**👉** **Electromagnetic Wave Equation**: The electromagnetic wave equation is a mathematical equation that describes the behavior of electromagnetic waves. It is given by the equation:

E = cB

where E is the electric field, B is the magnetic field, and c is the speed of light.

The electromagnetic wave equation demonstrates the relationship between the electric and magnetic fields in an electromagnetic wave. It shows that the electric and magnetic fields are perpendicular to each other and to the direction of the wave’s propagation.

**Check Also : **

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## Moving charges and Magnetism class 12 handwritten notes

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## Importance of Moving Charges and Magnetism Notes

There is one chapter of class 12 physics called Moving Charges and Magnetism. This chapter is very important for all students who are studying in class 12. One or two questions are often asked in class 12 Board exams. This chapter is not only important for board exams but also for IIT or NIT like competitive exams.

## Topics Covered in Magnetic effect of current and Magnetism

- Ampere’s swimming rule
- Magnetic Field
- An expression for the force on moving charge in the magnetic field
- Direction of force
- Fleming’s left-hand rule
- Biot-savart’s Law
- Relation b/w Biot-savart law for magnetic field and coulomb’s law for electrostatic Field
- Magnetic field due to Straight wire carrying current
- The direction of Magnetic Field
- Right-hand thumb rule
- The magnetic field at the center of a circular coil carrying current
- The direction of the Magnetic field
- The magnetic field at a point on an axis of a circular coil carrying current
- Ampere’s circuital law
- Proof of Ampere’s circuital law taking any arbitrary closed path
- Applications of Ampere’s circuital law
- Magnetic field due to an infinitely long straight wire carrying current
- Magnetic field due to current through a very long circular cylinder
- The solenoid
- Toroid
- The motion of the charged particle in a uniform electric field
- The motion of the charged particle in a uniform magnetic field
- Lorentz force
- Cyclotron
- Maximum Energy of positive ion
- Force on a current-carrying conductor placed in Magnetic Field
- The force between 2 parallel linear conductors
- Torque on a current-carrying coil in Magnetic Field
- Moving Coil Galvanometer
- Current Sensitivity
- Voltage sensitivity
- Shunt
- Ammeter
- Voltmeter

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