CBSE Class 12 Physics Notes Chapter 4 Moving Charges and Magnetism

Imagine a world where invisible forces dance around, pulling and pushing at objects without ever touching them. When charged particles start moving, they create a ripple effect in the fabric of space. This ripple is called a magnetic field, surrounding the moving charge and exerting force on other charged particles within its reach.

• Imagine a pebble tossed into a still pond. The ripples spread outwards, influencing the movement of other objects on the surface. 
• Similarly, the moving charge is the pebble, and the magnetic field is the ripple, influencing the paths of other charged particles nearby.
• The magnetic field can actually pull or push on other charged particles depending on their "charge personality." 
• Like poles attract, while opposite poles repel. 
• From the compass guiding your way to the speaker vibrating in your phone, the hum of your electric motor to the mesmerizing aurora borealis dancing across the night sky – all these are powered by the invisible dance of moving charges and the magnetic fields they create.

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Class 12 Physics Chapter 4 Notes - Moving Charges and Magnetism

Magnetic Force

• Magnetic force is the force exerted by a magnetic field on a moving charge.
• The direction of the magnetic force is perpendicular to both the velocity of the charged particle and the magnetic field.
• Formula:

F_m = qvB sinθ

Where

• Where Fm is the magnetic force
• q is the magnitude of the charge.
• v is the velocity of the moving charge.
• B is the magnetic field
• θ is the angle between velocity and magnetic field.

Magnetic Force

Magnetic Field, Lorentz Force

• Magnetic Field: The magnetic field is a region surrounding a magnet or a current-carrying conductor where magnetic forces influence charged particles' motion.
• Lorentz Force: The Lorentz Force is the force experienced by a charged particle moving in a magnetic field, perpendicular to both the particle's velocity and the magnetic field lines. 
  • This force is essential in understanding the interaction between charged particles and magnetic fields.

Magnetic Field, Lorentz Force

Magnetic Force On A Current-Carrying Conductor

• When a current flows through a conductor in the presence of a magnetic field, the conductor experiences a magnetic force perpendicular to both the current direction and the magnetic field.
• This phenomenon, described by the right-hand rule, is fundamental in various applications, including the operation of electric motors and the functioning of devices like loudspeakers. 
• The strength of the force depends on the current intensity, the conductor's length, and the magnetic field's strength.
• Formula:

F_m = BIL sinθ

Where

• Where Fm is the magnetic force
• L is the length of the conductor.
• I is the current flowing through the conductor.
• B is the magnetic field
• θ is the angle between the direction of current and magnetic field.

Magnetic Force On A Current-Carrying Conductor

Permittivity

• Definition: Permittivity is a material property indicating its ability to allow the electric field to pass through.
• Measurement: Expressed by the symbol ε, measured in Farads per meter (F/m).
• Role: Determines how much an electric field can be established within a material.

Permeability

• Definition: Permeability is a material property indicating its ability to allow the magnetic field to pass through.
• Measurement: Denoted by the symbol μ, measured in Henrys per meter (H/m).
• Importance: Influences the extent to which a material can be magnetised in the presence of a magnetic field.

Motion In A Magnetic Field

• Charged particles exhibit curved trajectories when moving through a magnetic field.
• The direction of the curvature is determined by the charge's polarity and the magnetic field orientation.
• A charged particle experiences a magnetic force perpendicular to both its velocity and the magnetic field direction.
• The force magnitude is given by the equation F=qvB, where q is the charge, v is the velocity, and B is the magnetic field strength.

Centripetal Force in Magnetic Field

• In circular motion within a magnetic field, the magnetic force acts as the centripetal force required to keep the particle in its curved path.
• This phenomenon is crucial in understanding the behaviour of charged particles in devices like cyclotrons and MRI machines.

Centripetal Force in Magnetic Field

Helical Motion Of Charged Particles And Aurora Borealis

• Helical motion refers to the spiral trajectory followed by charged particles in a magnetic field.
• Charged particles from the solar wind, spiraling along Earth's magnetic field lines, create the mesmerizing light display known as the Aurora Borealis.
• Earth's magnetic field guides charged particles towards the polar regions, where interactions with the atmosphere produce the luminous phenomenon of the Northern Lights.

Helical Motion Of Charged Particles And Aurora Borealis

Motion In Combined Electric And Magnetic Fields

• Charged particles experience motion influenced by both electric and magnetic fields simultaneously.
• Employed in devices like cyclotrons, where particles move in a circular path due to perpendicular electric and magnetic fields.

Velocity Selector

• A device allowing particles with specific velocities to pass through, achieved by balancing electric and magnetic forces.
• Ensures that only particles with a particular velocity, determined by the settings of electric and magnetic fields, continue along a defined path.

Velocity Selector

Cyclotron

• A type of particle accelerator in which charged particles spiral outward while being accelerated between electric and magnetic fields.
• Widely used in scientific research, particularly for accelerating particles in various fields such as nuclear physics and medical applications.

Cyclotron

Magnetic Field Due To A Current Element, Biot-Savart Law

• A current element, represented by a short section of a current-carrying conductor, produces a magnetic field.
• The Biot-Savart Law mathematically describes the magnetic field generated by a current element at a specific point in space.
• dB = μ₀ / (4π) * (Idl × r) / r²

Magnetic Field Due To A Current Element, Biot-Savart Law

Magnetic Field On The Axis Of A Circular Current Loop

• The magnetic field strength on the axis of a circular current loop is directly proportional to the current flowing through the loop.
• The magnetic field strength decreases with an increase in the distance from the center of the circular current loop along its axis, following an inverse square law.
• Formula:

B = (μ_o/4π) [(2πNIR²)/(R² + x²)^3/2]

Where

• B is the magnetic field strength on the axis of a circular loop.
• R is the radius of the circular loop
• x is the distance from center of the loop.
• N is the number of turns.
• I is the current flowing through the coil.

Ampere’s Circuital Law

• Ampere’s Circuital Law relates the magnetic field around a closed loop to the current passing through the loop.
• It is expressed as 

∮ B · dl = μ₀I

Where

• ∮ B · dl is the line integral of the magnetic field along a closed loop
• μ₀ is the permeability of free space, and 
• I is the current passing through the loop.

Ampere’s Circuital Law

The Solenoid 

• A solenoid is a coil of wire wound in the form of a cylinder, producing a strong and uniform magnetic field inside when an electric current flows through it.
• Solenoids are commonly used in devices such as electromagnetic locks, relays, and as components in electronic circuits.

Toroid

• A toroid is a solenoid wound into a circular or doughnut shape, with the wire coiled around a closed-loop core.
• Toroids exhibit enhanced magnetic properties, providing better magnetic confinement and reduced external field interference compared to straight solenoids.

Magnetic Confinement

• Magnetic confinement involves using strong magnetic fields to confine charged particles, typically in plasma, preventing their escape.
• Magnetic confinement is crucial in fusion research, where it helps contain and control high-temperature plasma to facilitate controlled nuclear fusion reactions.

Force Between Two Parallel Currents

• Currents flowing in the same direction attract each other, while currents in opposite directions repel, governed by Ampere's force law.
• The force between parallel currents is inversely proportional to the distance between the conductors, following a logarithmic relationship.

Force Between Two Parallel Currents

Roget’s Spiral For Attraction Between Parallel Currents

• Roget’s Spiral provides a visual representation of the varying force between parallel currents as a function of their separation distance.
• It aids in understanding the changing nature of the force, depicting how it evolves concerning the distance between the parallel current-carrying conductors.

Torque On Current Loop, Magnetic Dipole

• When a current-carrying loop is placed in a magnetic field, it experiences a torque, causing it to rotate.
• The torque on the current loop is proportional to its magnetic dipole moment and the strength of the magnetic field, providing a measure of its magnetic orientation.

Torque On A Rectangular Current Loop In A Uniform Magnetic Field

• The torque experienced by a rectangular current loop depends on its orientation relative to the magnetic field, with maximum torque when the plane of the loop is perpendicular to the field.
• The torque (τ) can be calculated using the formula τ=BIANsinθ, where B is the magnetic field strength, I is the current, A is the area of the loop, N is the number of turns, and θ is the angle between the normal to the loop and the magnetic field.

Circular Current Loop As A Magnetic Dipole

• A circular current loop behaves like a magnetic dipole, with a magnetic dipole moment (μ) directed perpendicular to the plane of the loop and proportional to the product of current (I) and loop area (πr²).
• The magnetic dipole moment of a circular loop is given by μ=Iπr², where I is the current and r is the radius of the loop. 
• The direction follows the right-hand rule, aligning with the direction of current flow.

The Magnetic Dipole Moment Of A Revolving Electron

• The revolving motion of an electron around its axis generates angular momentum, contributing to its magnetic dipole moment.
• The magnetic dipole moment of a revolving electron is quantized, aligning with the principles of quantum mechanics and discrete energy states.

The Magnetic Dipole Moment Of A Revolving Electron

Moving Coil Galvanometer

• The moving coil galvanometer is a device designed for detecting and measuring electric currents in a circuit.
• Consists of a coil in a magnetic field, allowing deflection with current flow.
• It operates based on the torque experienced by a coil carrying current in a magnetic field, resulting in a rotational movement proportional to the current strength.

Moving Coil Galvanometer

In conclusion, Units 3 and 4 collectively hold significant weightage, contributing to a total of 17 marks in the CBSE Class 12 Physics Exam 2024. Unit 3 focuses moving charges and magnetism and magnetic effects of current. Chapters 4 and 5 delve into the dynamic concepts of moving charges and magnetic fields. Unit 4, centred around electromagnetic induction and alternating currents, introduces the principles of generating electric currents through changing magnetic fields. 

There are Some important List Of Top Physics Questions On Moving Charges And Magnetism Asked In CBSE CLASS XII