Figure 28-33 shows a current loop A B C D E F A carrying a...

Figure 28-33 shows a current loop $A B C D E F A$ carrying a current $i=3.00 \mathrm{~A}$. The sides of the loop are parallel to the coordinate axes shown, with $A B=20.0 \mathrm{~cm}$, $B C=30.0 \mathrm{~cm}$, and $F A=10.0 \mathrm{~cm}$. In unit-vector notation, what is the magnetic dipole moment of this loop? (Hint: Imagine equal and opposite currents $i$ in the line segment $A D ;$ then treat the two rectangular loops $A B C D A$ and $A D E F A$.)

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Key Concepts

Magnetic Dipole Moment

This is a vector quantity that represents the strength and orientation of a magnetic source, such as a current loop. It is defined as the product of the current and the area vector of the loop, where the area vector has a magnitude equal to the area of the loop and a direction given by the right-hand rule.

Current Loop

A current loop is a closed circuit through which electrical current flows. It produces a magnetic field with a dipole-like structure. The characteristics of the magnetic field depend on the shape, size, and orientation of the loop.

Right-Hand Rule

This is a convention used to determine the direction of vector quantities such as the magnetic dipole moment in a current loop. By curling the fingers of the right hand in the direction of current flow, the thumb then points in the direction of the area vector or magnetic moment.

Unit Vector Notation

This is a method of expressing vectors in terms of components along predetermined coordinate axes (usually denoted by i, j, and k). It allows for clear representation and calculation of vector quantities in a standardized format.

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