Moving Charges And Magnetism Class 12 Notes

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Moving Charges And Magnetism Class 12 Notes

Understanding the principles of moving charges and magnetism is a crucial part of the Class 12 Physics curriculum. These topics form the foundation for many concepts in electromagnetism and modern electrical engineering. From the magnetic force on a current-carrying conductor to the application of Ampere’s Circuital Law, each subtopic builds a deeper understanding of how electric currents create magnetic fields and how those fields interact with materials. For students aiming to excel in exams like the CBSE boards or competitive engineering tests, mastering these concepts through clear notes and solved problems is essential.

Concept of Moving Charges

Electric Current and Magnetic Fields

When an electric charge moves, it produces a magnetic field around its path. This relationship was first discovered through Oersted’s experiment, where a compass needle deflected when placed near a wire carrying current. This shows that electricity and magnetism are interrelated, forming the basis of electromagnetism.

Right Hand Thumb Rule

The direction of the magnetic field generated by a current-carrying conductor is given by the Right-Hand Thumb Rule. If the thumb of your right hand points in the direction of the current, the curled fingers show the direction of the magnetic field around the wire.

Magnetic Force on a Moving Charge

Lorentz Force

When a charge q moves with velocity v in a magnetic field B, it experiences a magnetic force F given by the formula:

F = q(v à B)

This force is perpendicular to both the velocity of the charge and the direction of the magnetic field. This phenomenon is the basis for many applications, such as cyclotrons and mass spectrometers.

Properties of Magnetic Force

  • The magnetic force does no work on the moving charge since it is always perpendicular to the velocity.
  • It changes the direction of motion but not the speed.
  • Maximum force occurs when velocity is perpendicular to the magnetic field.
  • Zero force when the velocity is parallel or antiparallel to the magnetic field.

Motion of Charged Ptopics in a Magnetic Field

Circular Motion of Charged Ptopics

When a charged ptopic enters a magnetic field at right angles, it moves in a circular path. The centripetal force required for circular motion is provided by the magnetic Lorentz force.

Formula for radius of the circular path:

r = mv / (qB)

Where:

  • m = mass of the ptopic
  • v = speed of the ptopic
  • q = charge
  • B = magnetic field

Applications of Circular Motion

  • Mass spectrometry
  • Ptopic accelerators (cyclotron)
  • Cathode ray tubes in old television screens

Magnetic Force on a Current-Carrying Conductor

Force on a Straight Conductor

When a conductor of length L carries a current I in a magnetic field B, the magnetic force is given by:

F = I(L Ã B)

This formula is useful for understanding the working of devices like electric motors and loudspeakers.

Force Between Two Parallel Conductors

If two conductors carry currents I₁ and I₂ and are placed a distance d apart, they exert magnetic forces on each other. If currents are in the same direction, the wires attract each other. If currents are opposite, they repel. The force per unit length is:

F/L = (μ₀/2π) à (I₁I₂/d)

Torque on a Current Loop in Magnetic Field

Magnetic Dipole Moment

A current-carrying loop behaves like a magnetic dipole. The magnetic moment (M) of a current loop is given by:

M = I Ã A

Where A is the area vector of the loop. The torque τ on the loop is given by:

τ = M à B

Applications of Torque

  • Galvanometers
  • Electric meters
  • Moving coil instruments

Ampere’s Circuital Law

Statement of the Law

Ampere’s law relates the magnetic field around a closed loop to the total current enclosed by the loop. It is mathematically given by:

∮ B · dl = μ₀Ienclosed

Applications of Ampere’s Law

  • Magnetic field due to a long straight conductor
  • Magnetic field inside a solenoid
  • Magnetic field inside a toroid

Problems and Solutions

Problem 1: Magnetic Force on a Moving Charge

Question: A proton with a charge of 1.6à 10⁻¹⁹ C moves at 2à 10⁶ m/s perpendicular to a magnetic field of 0.1 T. Find the magnetic force.

Solution:

F = qvB = (1.6à 10⁻¹⁹)(2à 10⁶)(0.1) = 3.2à 10⁻¹⁴ N

Problem 2: Radius of Circular Path

Question: An electron (mass = 9.1à 10⁻³¹ kg, charge = 1.6à 10⁻¹⁹ C) moves at 10⁷ m/s in a magnetic field of 0.01 T. Find the radius of its circular path.

Solution:

r = mv / (qB) = (9.1à 10⁻³¹ à 10⁷) / (1.6à 10⁻¹⁹ à 0.01) ≈ 5.7à 10⁻³ m

Problem 3: Force Between Two Conductors

Question: Two wires 5 cm apart carry currents of 3 A and 4 A in the same direction. Find the force per unit length.

Solution:

F/L = (μ₀/2π) à (I₁I₂/d)

= (4πà 10⁻⁷ / 2π) à (3à 4 / 0.05)

= 2à 10⁻⁷ à 240 = 4.8à 10⁻⁵ N/m

Conclusion and Study Tips

Mastering moving charges and magnetism requires conceptual clarity and regular practice of numerical problems. Understand the physical meaning behind each formula and apply the right-hand rules to visualize directions. Focus on derivations, understand the assumptions, and practice previous year questions to prepare effectively for exams. Keeping well-organized class 12 notes on magnetism and moving charges will help consolidate your understanding and improve recall under exam conditions.