Magnetic Dipoles

Section 28.1 Magnetic Dipoles

Activity 28.1.1. Warm-up Activity.

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Shown below are two bar magnets. Predict how they will interact with one another. What will happen to their motion?

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Figure 28.1.1. Two bar magnets sit side by side, with their south poles facing each other.
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The magnetic dipole moment, symbolized by \(\vec{\mu}\text{,}\) represents the strength and orientation of objects like permanent magnets.

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The dipole moment is a physical property of the permanent magnet.
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The dipole moment points from the south to the north pole inside the permanent magnet.
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The magnitude of the dipole moment is related to the strength of the magnet.
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A permanent magnet with a dipole moment will create a magnetic field such as the one shown in the figure below.
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A bar magnet with a north and south pole. The field lines come out of the north pole and curve out and around to the south pole. — Figure 28.1.4. *Example:* Magnetic field lines created by a permanent magnet.
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Assumption 28.1.5. Magnetic Moment for a Current Loop.

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Current loops also behave as if they are permanent magnets!

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A loop with area \(A\) carrying current \(I\) may be approximated as having a magnetic dipole moment

\begin{equation*} \mu = IA \end{equation*}

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The direction of the dipole moment is the same as the direction of the magnetic field at the center of the loop, which can be found using a right hand rule: curl your fingers in the direction of the current, and your right thumb will point in the direction of \(\vec{\mu}\text{.}\)

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A tilted loop carrying current I when viewed from the top right. The magnetic dipole moment points up and to the right inside an imaginary bar magnet with its north pole in the upper right and its south pole in the lower left. — Figure 28.1.6. *Example:* A loop carrying current counterclocwise when viewed from the top right. The magnetic dipole moment of the loop and its north and south poles are represented in gray.
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Subsubsection Activities

Activity 28.1.2. Current Loop and Bar Magnet.

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The figure below shows a bar magnet and a loop with current that is running clockwise when viewed from above.

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A bar magnet sits above a loop of current that is running clockwise when viewed from above. The north pole is closest to the loop of current. — Figure 28.1.7. A bar magnet and a current loop.
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What direction is the magnetic dipole moment of the current loop? What direction is the net force on the bar magnet?

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Solution.

Anything with a magnetic moment both creates a magnetic field and experiences magnetic forces! Modeling the loop as a bar magnet gives the picture below, which suggests a downward force on the bar magnet (the bar magnet’s north pole is attracted to the “south pole” of the current loop).

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