11.2 Magnetic Fields and Lines

Magnetic fields are invisible forces that affect moving electric charges. They're all around us, from Earth's magnetic field guiding compasses to the fields in your phone's speakers. Understanding how they work is key to grasping electromagnetism.

Magnetic field lines help us visualize these forces. They show the field's direction and strength, always forming closed loops. This concept is crucial for understanding how magnets and electric currents create and interact with magnetic fields.

Magnetic Fields and Lines

Definition of magnetic fields

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• A region in space where a moving electric charge experiences a force due to its motion
• The force experienced by a moving charge in a magnetic field is called the magnetic force ($\vec{F}_B$)
• Magnetic force on a moving charge is given by $\vec{F}_B = q\vec{v} \times \vec{B}$
  • $q$ represents the charge of the particle
  • $\vec{v}$ represents the velocity of the charge
  • $\vec{B}$ represents the magnetic field vector
• Magnitude of the magnetic force is $F_B = qvB\sin\theta$
  • $\theta$ is the angle between the velocity vector and the magnetic field vector
• Magnetic force is always perpendicular to both the velocity and magnetic field vectors (right-hand rule)
• SI unit for magnetic field strength is the tesla (T)
  • 1 T = 1 N/(A·m)
• Examples of magnetic fields:
  • Earth's magnetic field (compass)
  • Magnetic fields generated by bar magnets or electromagnets

Right-hand rule for magnetic forces

• Determines the direction of the magnetic force on a moving charge using the right hand
• For a positively charged particle:
  • Point right thumb in the direction of the particle's velocity ($\vec{v}$)
  • Curl fingers in the direction of the magnetic field ($\vec{B}$)
  • Palm points in the direction of the magnetic force ($\vec{F}_B$)
• For a negatively charged particle, the magnetic force direction is opposite to that determined by the right-hand rule for a positive charge
• Consistent with the cross product in the magnetic force equation $\vec{F}_B = q\vec{v} \times \vec{B}$
• Examples:
  • Determining the direction of force on a proton moving through a magnetic field
  • Predicting the motion of an electron beam in a cathode-ray tube (CRT)
• The combination of electric and magnetic forces on a charged particle is known as the Lorentz force

Visualization of magnetic field lines

• Visual representation of the magnetic field in space
• Properties of magnetic field lines:
  • Direction of the magnetic field at any point is tangent to the field line
  • Density of field lines indicates the strength of the magnetic field
    • Closely spaced lines represent a strong magnetic field
    • Widely spaced lines represent a weak magnetic field
  • Always form closed loops, starting and ending at the source of the magnetic field
    • Never cross or diverge
• Magnetic field lines for a bar magnet:
  • Exit the north pole and enter the south pole
  • Field is strongest near the poles, where lines are most dense
• Magnetic field lines for a current-carrying wire:
  • Form concentric circles around the wire
  • Direction determined by the right-hand rule for a current-carrying wire
    1. Grasp the wire with your right hand
    2. Point thumb in the direction of the current
    3. Fingers will curl in the direction of the magnetic field lines
• Examples:
  • Sketching field lines around a bar magnet
  • Visualizing the magnetic field generated by a solenoid or a toroid

Magnetism and Related Phenomena

• Magnetism is the fundamental force responsible for the behavior of magnetic fields and their interactions with charged particles and materials
• Electromagnetic induction is the process by which a changing magnetic field induces an electric current in a nearby conductor
• Ferromagnetism is a type of magnetism where certain materials (like iron) can become permanently magnetized and exhibit strong magnetic properties