Question

What equations can be obtained from a Magnetic field gradient vs Magnetic force on dipole graph? What does the slope represent? This is for the Magnetic force on a magnet experiment.

Answer 1

a) The following can be understood by the graph,

• Net magnetic force on a magnetic dipole is 0 in a region of uniform magnetic field.
• There exists some net magnetic force experienced by the magnetic dipole in a region of non-uniform magnetic field (ie. in the presence of magnetic fiels gradient).

The magnetic moment can be determined by the graph as,

, where is magnetic force

   is magnetic dipole moment

is magnetic field

Note : (Both and are under the gradient sign)

The torque can further be determined from the above equation as,

, where is the torque

   is the magnetic field moment

   is the magnetic field

b) The slope of the graph determines the magnetic dipole moment.

   , where is magnetic force

is magnetic dipole moment

   is magnetic field

Both and are under the gradient sign thus giving a relation between magnetic field gradient and magnetic force.