Lecture 37: Ampere's Law Numerical Problems & Force Between Parallel Currents | Dr. Imran Malik

Ampère's Law, Parallel Currents, Solenoid & Toroid | Physics Lecture 37 This lecture continues the study of Magnetism with a detailed discussion of Ampère's Law and its applications. Students will develop a deeper understanding of the mathematical formulation of Ampère's Law and learn how to apply it to solve magnetic field problems involving highly symmetric current distributions. The lecture also explores the interaction between parallel current-carrying conductors, explaining the origin of attractive and repulsive magnetic forces between currents. The lecture concludes with an introduction to solenoids, toroids, and the tokamak, providing students with a preview of important engineering applications of magnetic fields. The lecture begins with a detailed revision of Ampère's Law, focusing on its mathematical expression and physical interpretation. Students learn how to select an appropriate Amperian loop, determine the direction of the differential length element d𝐥, identify the enclosed current, and simplify the line integral using symmetry. The conditions under which Ampère's Law is applicable are discussed, along with comparisons to Gauss's Law and the Biot–Savart Law. A major portion of the lecture is devoted to solving step-by-step numerical problems on Ampère's Law. Students apply the law to determine magnetic fields in highly symmetric geometries while developing examination-oriented problem-solving techniques. The lecture then introduces the interaction between parallel current-carrying conductors. Using the magnetic field produced by one conductor, students derive the force acting on a second conductor and explain why parallel currents attract while anti-parallel currents repel. The physical origin of this interaction and its importance in electrical engineering are discussed in detail. Numerous conceptual examples and numerical problems strengthen understanding of this important phenomenon. The lecture concludes with a brief introduction to the solenoid, toroid, and tokamak. Students learn the basic structure and purpose of these devices, preparing them for the detailed derivations and applications presented in the following lectures. The role of magnetic confinement in a tokamak and its significance in controlled nuclear fusion are also briefly discussed. Throughout the lecture, mathematical derivations, conceptual discussions, graphical illustrations, and examination-oriented numerical problems help students build a strong foundation in magnetostatics and magnetic field applications. Topics Covered Review of Ampère's Law Mathematical Form of Ampère's Law Physical Interpretation of Ampère's Law Amperian Loop Differential Length Element (d𝐥) Enclosed Current Symmetry in Ampère's Law Numerical Problems on Ampère's Law Magnetic Interaction Between Parallel Conductors Force Between Parallel Current-Carrying Wires Parallel Currents Attract Anti-Parallel Currents Repel Numerical Problems on Parallel Currents Introduction to Solenoids Introduction to Toroids Introduction to Tokamak Engineering Applications of Magnetic Fields Examination-Oriented Problem Solving Techniques Recommended Textbooks Physics for Scientists and Engineers — Raymond A. Serway and John W. Jewett, Jr. University Physics with Modern Physics — Hugh D. Young and Roger A. Freedman Fundamentals of Physics — David Halliday, Robert Resnick, and Jearl Walker This lecture is part of PHY-101 and PHY-102 (Basic Physics) courses for undergraduate students. Keywords Ampère's Law, Ampere's Law, Amperian Loop, Magnetic Field, Parallel Current-Carrying Wires, Force Between Parallel Currents, Parallel Currents Attract, Anti-Parallel Currents Repel, Magnetostatics, Solenoid, Toroid, Tokamak, Magnetic Force Between Wires, Electromagnetism, Engineering Physics, University Physics, Physics Lecture, Basic Physics, PHY-101, PHY-102, Physics Tutorial #Physics #AmpèresLaw #AmpereLaw #ParallelCurrents #MagneticField #Solenoid #Toroid #Tokamak #Magnetism #Electromagnetism #EngineeringPhysics #UniversityPhysics #PhysicsLecture #PHY101 #PHY102 #STEM