Magnetic Dipole Moment

Claimed by Guillermo Bacardi

The magnetic dipole moment of a loop of current may be considered to be a measure of the strength of the magnetic field. The magnetic field generated by a magnet points from south to north and is proportional to its magnetic dipole moment. In a loop of current the magnetic dipole moment is a vector that is perpendicular to the loop and can be found using the right-hand-rule. The magnetic dipole moment is a measure of the strength of the magnetic dipole.

The Main Idea

The main idea for this topic is to define the magnetic dipole moment and distinguish from the magnetic dipole.

A Mathematical Model

The magnetic dipole moment is represented by µ. This is set equal to the current running through the wire multiplied by the area of the circular loop. Here the area of the circular loop is defined as πR^2. The units for the magnetic dipole moment are amperes times meters squared.

[math]\displaystyle{ \boldsymbol{\mu} = \boldsymbol{I} \times\mathbf{A} }[/math]

If there is more than one coil in the loop then all of the coils must be accounted for by a value N that represents all of the coils.

[math]\displaystyle{ \boldsymbol{\mu} = \boldsymbol{NI} \times\mathbf{A} }[/math]

The overall equation for a magnetic field turns into

[math]\displaystyle{ \mathbf{B} = \frac{\mu_0}{4\pi}\frac{2\mu}{R^3} }[/math]

A Computational Model

How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript

Examples

Simple

What is the magnetic dipole moment of a 1200 turn circular coil that has a radius of 10 cm and carries a current of 2 amperes?

Solution: µ=NIA N=1200 I = 2 A = π0.1^2

       So µ = (1200)(2)(0.0314) = 75.4 Am^2

Difficult

What is the magnetic field at a point 3m away from a coil that has 250 turns, a radius of 2m and a current of 4 amperes running through it?

First step is to calculate the dipole moment using µ=NIA. In this situation N=250, A = 4

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