In Fig. 28-51 a, two concentric coils, lying in the same...

In Fig. $28-51 a$, two concentric coils, lying in the same plane, carry currents in opposite directions. The current in the larger coil 1 is fixed. Current $i_{2}$ in coil 2 can be varied. Figure $28-51 b$ gives the net magnetic moment of the two-coil system as a function of $i_{2}$. The vertical axis scale is set by $\mu_{\text {nets }}=2.0 \times 10^{-5} \mathrm{~A} \cdot \mathrm{m}^{2}$, and the horizontal axis scale is set by $i_{2 s}=10.0 \mathrm{~mA}$. If the current in coil 2 is then reversed, what is the magnitude of the net magnetic moment of the two-coil system when $i_{2}=7.0 \mathrm{~mA}$ ?

Key Concepts

Magnetic Moment

The magnetic moment is a vector quantity that characterizes the strength and orientation of a magnetic source, such as a current-carrying loop. It is typically calculated as the product of the current and the area of the loop, and it determines the torque experienced by the loop in an external magnetic field.

Superposition of Magnetic Moments

When more than one magnetic moment is present, for instance from multiple coils, the net magnetic moment is obtained by vectorially adding the individual moments. This principle of superposition is essential when analyzing systems where the magnetic effects of different currents interact, potentially leading to partial cancellation or reinforcement.

Effect of Current Direction on Magnetic Moment

The direction of the magnetic moment of a current loop is determined by the direction of the current flow according to the right-hand rule. Reversing the current in a coil reverses the direction of its magnetic moment, leading to different interactions when combined with moments from other coils. In systems with opposing currents, these directional changes are crucial for determining the overall magnetic effect.

Graphical Scaling and Data Interpretation

Interpreting experimental graphs often involves understanding how physical quantities are scaled and represented. Scaling factors set on the axes help in translating graphical data into real-world measurements, enabling accurate calculation of the net magnetic moment or other related physical quantities based on standardized units.

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