Magnetic Fields and Forces Summary

Magnets and Magnetism

  • Permanent magnets attract unmagnetized iron objects and other magnets.
  • Like poles repel, and opposite poles attract.
  • Earth is a magnet; its north geographic pole is near a magnetic south pole.
  • Magnetic declination: deviation between magnetic north and geographic north.
  • Magnetic inclination: angle of the magnetic field relative to Earth's surface.
  • Magnetic poles come in pairs; magnetic monopoles have not been found.

Magnetic Fields

  • Moving charges (current) create magnetic fields.
  • Magnetic field exerts a force on other moving charges.
  • The symbol for magnetic field is \vec{B}.
  • The direction of \,vec{B} is the direction the north pole of a compass needle points.

Magnetic Force on a Moving Charge

  • The magnetic force magnitude is proportional to the velocity component perpendicular to the field.
  • Zero force if the charge is at rest or moving parallel to the field.
  • Maximum force when charge moves perpendicular to the field: F_{max} = qvB
  • Magnetic force as a vector product: \vec{F} = q \vec{v} \times \vec{B}
  • The magnetic force is perpendicular to the plane containing \,vec{v} and \,vec{B}.
  • Use the right-hand rule (RHR) to determine the direction of the force on a positive charge.
  • For negative charges, the force direction is opposite to that given by the RHR.

Right-Hand Rule

  • Place the velocity and magnetic field vectors tail to tail.
  • Imagine turning \,vec{v} toward \,vec{B} in the \,vec{v}-\,vec{B} plane (through the smaller angle).
  • The force acts along a line perpendicular to the \,vec{v}-\,vec{B} plane.
  • Curl the fingers of your right hand around this line in the same direction you rotated \,vec{v}.
  • Your thumb now points in the direction the force acts.