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.