LECTURE NOTES 5 - MAGNETISM_7ddc765f1a920d8c13eda5cb8b5677eb

5. Magnetism

5.1 Overview of Concepts

This chapter covers several core principles of magnetism, including electric charges and their related fields, electric potential, electric current, direct and alternating currents, electromagnetic induction, as well as concepts in geometric and physical optics. These topics build on each other and form the foundational elements of magnetism and its applications.

5.2 Magnetic Elements

  • Definition of Magnets: Magnets possess two poles - a north pole and a south pole. Due to the nature of magnetism, like poles will repel each other, while unlike poles attract. It is essential to remember that magnetic poles cannot be isolated as stand-alone entities.

  • Ferromagnetic Materials: Materials that exhibit significant magnetic properties are known as ferromagnetic materials, and they include iron, cobalt, nickel, and gadolinium.

5.3 Magnetic Fields and Directions

  • Magnetic Field Lines: For a bar magnet, magnetic field lines emerge from the north pole and into the south pole, forming closed loops. This helps visualize the direction and strength of the magnetic field created by the magnet itself (refer to Fig. 5.2).

  • Right-Hand Rule: The direction of the magnetic field surrounding a current-carrying wire can be determined by the right-hand rule (RHR). When the thumb points in the direction of the current, the curled fingers indicate the direction of the magnetic lines of force.

5.4 Magnetic Force on Moving Charges

  1. Magnetic Force Calculation: The magnetic force (F) experienced by a charge moving through a magnetic field (B) is calculated using the equation:

    [ F = q v B \sin \theta ]

    where:

    • ( q ) = charge (C)

    • ( v ) = velocity of the particle (m/s)

    • ( B ) = magnetic field strength (T)

    • ( \theta ) = angle between the velocity vector and the magnetic field direction.

  2. Force Directions: Using the right-hand rule, if the charge is positive, the force will be directed perpendicular to both the velocity and the magnetic field direction.

5.5 Current-Carrying Wires in Magnetic Fields

  • Force on Wires: When an electric current flows through a conductor placed in a magnetic field, the conductor experiences a force. This force is given by:

    [ F = I L B \sin \theta ]

    where:

    • ( I ) = current (A)

    • ( L ) = length of the wire segment in the field (m)

    • ( B ) = strength of the magnetic field (T).

5.6 Solenoids and Electromagnets

  • Solenoids: A solenoid is a coil of wire designed to produce a uniform magnetic field when an electric current passes through it. The intensity of the magnetic field inside a solenoid can be calculated using Ampere's Law:

    [ B = \mu_0 \frac{N I}{L} ]

    where:

    • ( \mu_0 ) = permeability of free space (T·m/A)

    • ( N ) = number of turns in the solenoid

    • ( I ) = current

    • ( L ) = length of the solenoid.

  • Applications of Electromagnets: Electromagnets are used in various devices including electric motors, galvanometers, magnetic locks, and more. The configuration and design vary depending on the specific application.

5.7 Example Problems

  1. Example 1: Calculating the magnetic force on an electron moving in a magnetic field, using the derived equations and substituting known values to find the speed.

  2. Example 2: Determining the magnetic force acting on a proton and then an electron in the same magnetic field to highlight the difference in their responses due to charge and mass variations.

  3. Example 3: Analyzing the forces on two parallel wires carrying current to illustrate concepts of attraction and repulsion in magnetic fields.

5.8 Summary

Magnetism plays a fundamental role in physics, particularly in electromagnetism. Understanding magnetic fields and forces is essential for various applications in technology and engineering. From basic concepts of magnetic poles to complex interactions in electric currents, this chapter provides a comprehensive overview of the principles that govern magnetism.