Amperes Circuital Law – Class 12 | Chapter – 4 | Physics Short Notes Series PDF for NEET & JEE

Amperes Circuital Law: Amperes Circuital Law is a fundamental principle in electromagnetism that relates the magnetic field around a closed loop to the electric current passing through the loop. The law states that the magnetic field at any point in space is proportional to the electric current passing through a closed loop that passes through that point. Ampere’s Circuital Law is one of the four Maxwell’s equations, which form the foundation of classical electromagnetism and are used to describe and understand the behavior of electromagnetic fields and waves.

Formula of Amperes Circuital Law

The Amperes Circuital Law is useful for calculating the magnetic field around conductors carrying electric current, such as wires and coils. It is also used to calculate the magnetic field produced by a solenoid, a type of coil commonly used in electrical and electronic devices.

Mathematically, Ampere’s Circuital Law can be expressed as:

∮B⋅dl = μ0 * Ienc

Where,

  • B is the magnetic field,
  • dl is a differential element of the closed loop,
  • Ienc is the total current enclosed within the loop, and
  • μ0 is the permeability of free space

Applications of Amperes Circuital Law

Amperes Circuital Law has many important applications in various fields, including electrical engineering, physics, and medicine. Some of the key applications are:

  • Electrical circuits: Ampere’s Circuital Law is used in the analysis of electrical circuits to calculate the magnetic field produced by current-carrying conductors and to determine the mutual inductance between two or more circuits.
  • Magnetic resonance imaging (MRI): Ampere’s Circuital Law is used in the design and operation of magnetic resonance imaging (MRI) systems, which use magnetic fields and radio waves to create images of the inside of the human body.
  • Electromagnetic devices: Ampere’s Circuital Law is used in the design of electromagnetic devices, such as transformers, inductors, and solenoids, to calculate the magnetic field produced by these devices and to optimize their performance.
  • Electromagnetic compatibility (EMC): Ampere’s Circuital Law is used in the analysis and design of electromagnetic compatibility (EMC) systems, which are designed to minimize the impact of electromagnetic interference on electronic devices and systems.
  • Electric motors and generators: Ampere’s Circuital Law is used in the design of electric motors and generators, which convert electrical energy into mechanical energy and vice versa, to calculate the magnetic field produced by the current in the conductors and to optimize their performance.

Limitations of Amperes Circuital Law

Amperes Circuital Law is a powerful tool for understanding and analyzing the behavior of magnetic fields, but like any scientific law, it has certain limitations. Some of the key limitations of Ampere’s Circuital Law are:

  • Limitations in space: Ampere’s Circuital Law is applicable only in the region where the magnetic field is a continuous function and its derivatives are well-defined. It is not applicable in regions where the magnetic field is discontinuous or where it is not well-defined.
  • Limitations in time: Ampere’s Circuital Law is a static law and does not take into account the time-varying nature of electric currents. It is not applicable to transient electromagnetic phenomena, such as electromagnetic pulses.
  • Limitations in material: Ampere’s Circuital Law is based on the assumption that the magnetic field is proportional to the current. This assumption is valid only for conductors with linear magnetic properties. It is not applicable to conductors with non-linear magnetic properties, such as ferromagnetic materials.
  • Limitations in accuracy: Ampere’s Circuital Law provides a good approximation of the magnetic field in many situations, but it is not always accurate. In some cases, more advanced theories, such as quantum mechanics, are required to provide a more accurate description of the magnetic field.


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By Team Learning Mantras