Two concentric, circular wire loops, of radii r1=20.0 cm and r2=30.0 cm, are located in an x y

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Two concentric, circular wire loops, of radii r1=20.0 cm...

Two concentric, circular wire loops, of radii $r_{1}=20.0 \mathrm{~cm}$ and $r_{2}=30.0 \mathrm{~cm}$, are located in an $x y$ plane; each carries a clockwise current of $7.00 \mathrm{~A}$ (Fig. $28-48$ ). (a) Find the magnitude of the net magnetic dipole moment of the system. (b) Repeat for reversed current in the inner loop.

Two concentric, circular wire loops, of radii $r_{1}=20.0 \mathrm{~cm}$ and $r_{2}=30.0 \mathrm{~cm}$, are located in an $x y$ plane; each carries a clockwise current of $7.00 \mathrm{~A}$ (Fig. $28-48$ ). (a) Find the magnitude of the net magnetic dipole moment of the system.
(b) Repeat for reversed current in the inner loop.

Key Concepts

Magnetic Dipole Moment

The magnetic dipole moment is a vector quantity that signifies the strength and orientation of a current loop’s magnetic field. It is calculated as the product of the current and the area enclosed by the loop. This concept is fundamental to understanding how current loops create magnetic fields and how these fields interact with external magnetic fields.

Current Loop Calculation

For a single circular loop, the magnetic dipole moment is determined by multiplying the current by the area of the circle (?r²). This formulation is essential when analyzing systems with one or more loops, as it allows each loop’s contribution to be computed individually based on its size and current.

Superposition Principle

In systems comprising multiple current loops, the overall magnetic dipole moment is found by summing the individual dipole moments vectorially. The direction of each dipole moment, determined by the current’s orientation (using the right-hand rule), is critical when combining contributions from different loops.

Current Direction and Sign Convention

The direction in which the current circulates in a loop determines the orientation of its magnetic dipole moment. Reversing the current in a loop reverses the direction of its dipole moment, which is a key consideration when evaluating the net effect in systems with loops carrying currents in different or opposing directions.

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