Lesson 8

Introduction to Magnetism

  • Magnetism is related to electric charges, specifically the motion of these charges (current).
  • Current-carrying charges exert forces on magnetic poles.

Magnetic Fields

  • The magnetic field (denoted as B-field) is defined to explain how a compass needle moves in response to a magnetic effect.
  • The B-field exists around a current-carrying wire, and is a vector field.
  • Properties of Magnetic Fields:
    • Direction: The force on a north pole is in the direction of the B-field vector, while the force on a south pole is opposite.
    • Representation: B-field lines parallel the B-field vector, indicating the direction of the field.

Types of Magnetic Fields

Moving Charges and Magnetic Fields

  • Both permanent magnets and magnetic effects from magnetic fields created by moving charges represent types of magnetism.
  • A moving charge creates a magnetic field while still generating an electric field.

Biot-Savart Law

  • The Biot-Savart Law describes the contribution of infinitesimal segments of a current-carrying wire to the total magnetic field.
  • To find the total magnetic field, one must integrate contributions from each segment along the wire.

Magnetic Field of a Long Wire

Example 1: Force Calculation

  • The force per unit length between two parallel wires carrying currents I1 and I2 can be calculated using their magnetic field interactions.

Example 2: Circular Section Field

  • To find the B-field at a point due to a circular segment of current-carrying wire, computations based on the Biot-Savart Law are used.

Ampere's Law

  • Provides a relationship between the magnetic field and the current through a long wire, reinforcing concepts from the Biot-Savart Law.

Solenoids

  • A solenoid is a tightly wound helical coil of wire that generates a uniform magnetic field when current flows through it.
  • Field Behavior:
    • Inside a long solenoid, the magnetic field becomes uniform and parallel to the solenoid's axis.
    • Outside the solenoid, the magnetic field approaches zero.

Example 1: Field Inside a Solenoid

  • Calculate the magnetic field strength inside a long solenoid based on its turns and current.

Example 2: Superconducting Solenoid

  • For a solenoid of length 2 m with 2000 turns, determine the required current for a magnetic field of 5 T at its center.

Magnetic Dipoles

Atomic Magnets

  • A current loop creates a magnetic field, functioning similarly to a magnetic dipole.
  • Dipole Moment: A vector pointing from the south to the north pole, indicating the polarity and strength of the magnetic loop.

Permanent Magnets

  • The atomic dipoles in materials are generally random, leading to no net magnetic field.
  • In ferromagnetic materials like iron, dipoles can align, creating a strong magnetic field.
  • The material can be magnetized by aligning its magnetic domains, thus creating a permanent magnet if the alignment persists.

Conclusion

  • Permanent magnets exhibit attraction due to their aligned magnetic domains, analogous to polarization from an electric field.
  • The ability for a material to retain aligned magnetic domains after an external field is dependent on its crystalline structure.