Ampere’s Circuital Law and Application - Steady Magnetic Field - Electromagnetic Field & Wave Theory

TL;DR

Ampere's Circuital Law states that the line integral of magnetic field intensity along a closed path is equal to the current enclosed by that path. It has applications in various current configurations such as filamentary current, coaxial cable, solenoid, and toroid.

Transcript

hello everybody i welcome you all to the subject electromagnetic field theory here we are in chapter number seven that is steady magnetic field and this is the twelfth video up till now in the steady magnetic fields we have seen the major topics that is currently distributions we know that the electric current that is dc current causes magnetic fie... Read More

Key Insights

• 😚 Ampere's Circuital Law relates the line integral of magnetic field intensity to the current enclosed by a closed path.
• 🚠 It is applicable to various current configurations, such as filamentary current, coaxial cable, solenoid, and toroid.
• 👮 The law provides a mathematical relationship to calculate magnetic field intensity in different scenarios.
• 🫥 Ampere's Circuital Law is based on the principle of magnetic flux lines and their circulation around current-carrying conductors.
• 💁 The law can be applied in both integral and differential forms, depending on the specific current configuration.
• ❓ Understanding Ampere's Circuital Law is essential in analyzing and designing systems involving electromagnets and inductors.
• 🏑 The applications of Ampere's Circuital Law in different current configurations help solve problems related to magnetic fields and current-carrying conductors.

Questions & Answers

Q: What is Ampere's Circuital Law?

Ampere's Circuital Law states that the line integral of magnetic field intensity along a closed path is equal to the current enclosed by that path.

Q: How is Ampere's Circuital Law applied to filamentary current?

In the case of filamentary current, the magnetic field intensity can be calculated using the formula h bar = i enclosed / (2πρ), where i enclosed is the current enclosed by the closed path and ρ is the radius.

Q: What is the application of Ampere's Circuital Law in a coaxial cable?

Ampere's Circuital Law can be applied to a coaxial cable to determine the magnetic field intensity inside and outside the cable. Inside the cable, the magnetic field intensity is given by h bar = i / (2πρa), where i is the total current flowing through the inner and outer conductors, ρ is the distance from the central axis, and a is the radius of the inner conductor.

Q: How is Ampere's Circuital Law applied to a solenoid?

In a solenoid, Ampere's Circuital Law can be used to calculate the magnetic field intensity inside the solenoid. The expression is h bar = n i / d, where n is the number of turns, i is the current flowing through the solenoid, and d is the dimension of the solenoid.

Summary & Key Takeaways

• The content discusses Ampere's Circuital Law, which describes the relationship between magnetic field intensity and current in a closed path.

• It explains how current distributions and biot savers law contribute to the production of a magnetic field.

• The content also covers the applications of Ampere's Circuital Law in different current configurations, such as filamentary current, coaxial cable, solenoid, and toroid.