Magnetic Fields and Moving Charges

Introduction to Magnetic Fields

• Magnetic fields affect moving charges.
• Defined by the effect they have on moving charges.

Visualizing Magnetic Fields

• Similar to electrostatic fields: use field lines.
• Field lines convention: draw from north to south pole.
• Hypothetical magnetic north monopole moves from north to south.
  • Path examples: curves around from north to south.
• Compass method: pointer tangent to field line.
  • Compass north pole seeks magnetic south.

Understanding North and South Poles

• North seeks south, similar to positive seeks negative.
• Magnetic fields always come in dipoles.
• Electrostatic forces can have monopoles (positive or negative charge).

Magnitude of Magnetic Field

• Determined by the effect on a moving charge.
• Magnetic force defined in terms of moving charge.
• Magnetic field (B) is a vector.
• Force on a moving charge:
  • Formula: F = q(v x B)
    • q: charge magnitude (can be positive or negative).
    • v: velocity of the charge.
    • B: magnetic field.
    • Cross product: v x B.
    • Force vector is perpendicular to both velocity and magnetic field.

Cross Product & Magnetic Field

• Cross product significant when vectors are perpendicular.
• No effect if velocity and magnetic field are parallel.
• Magnetic field affects charge only if perpendicular to velocity.
• Force is perpendicular to both velocity and magnetic field.

Units of Magnetic Field

• Force unit: newtons.
• Charge unit: coulombs.
• Velocity unit: meters per second.
• Magnetic field units: newtons per coulomb meter or newton seconds per coulomb meter.
• Named after Nikola Tesla: 1 tesla (T) = 1 newton second per coulomb meter.

Summary

• Magnetic forces are distinct yet related to electrostatic forces.
• Magnetic fields are visualized with field lines from north to south.
• Defined by their effect on moving charges.
• Units reflect their interaction with moving charges.