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# Magnetic Dipoles

"A fact is a simple statement that everyone believes. It is innocent, unless found guilty. A hypothesis is a novel suggestion that no one wants to believe. It is guilty, until found effective"
Edward Teller

- Shown below is a rectangular current loop sides a and b placed in a region of space with uniform magnetic field (B).

- Application of the expression for the force on a current carrying wire to the top and bottom sides of the rectangle leads to cancellation of forces as shown.

- The forces on the other two sides (length a) are also equal and opposite, as shown in (b) above, . Although the net force in this case is zero, because the forces are not co-linear, there is a net torque on the current loop, given by

> The magnitude of this torque is given by
> where A = ab is the cross section area of the coil.

- The magnitude of the magnetic dipole moment of the loop with N turns is defined by,

> μ is a vector quantity whose direction is perpendicular to the loop with a sense defined by (another) Right Hand Rule.

- With this definition of μ the torque on the current loop is given by

- Without proof, the potential energy of a magnetic dipole in an external magnetic field is given by

Note that the above expressions for the torque and potential energy of a magnetic dipole in an external magnetic field are identical in form to those obtained for an electric dipole in an external electric field.
and

I stayed up all night to see where the sun went. Then it dawned on me.

Dr. C. L. Davis
Physics Department
University of Louisville
email: c.l.davis@louisville.edu