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A current-carrying loop acts like a tiny magnet. It creates a magnetic dipole moment, which is a measure of its magnetic strength and orientation. Imagine you have a loop of wire, like the ones in the exercise. When current flows through it, a magnetic field is generated around it. This is much like how electric flow creates a magnetic field in a straight wire but, in the case of a loop, the effect is more pronounced.
The magnetic moment of the loop is a result of both the current flowing through the wire and the area the loop covers. In simple terms, the bigger the loop or the stronger the current, the larger the magnetic moment. This concept is essential in understanding how we calculate the net magnetic moment in the given exercise.

• The direction of the magnetic moment depends on the direction of the current. Clockwise and counterclockwise currents will produce magnetic moments pointing in opposite directions.
• This principle is very useful in technologies like electric motors and generators.

The area of a circle is a fundamental concept in geometry and physics, especially when dealing with circular loops. It is determined using the formula \( A = \pi r^2 \), where \( A \) represents the area, \( \pi \) is a constant (approximately 3.14159), and \( r \) is the radius of the circle.
In the exercise, two different loops are considered, each with its own radius.

• For the inner loop, with a radius of 20 cm, we convert it to meters (0.2 m) for calculations. The resulting area is \( A_1 = \pi (0.2)^2 = 0.04\pi \text{ m}^2 \).
• For the outer loop, with a radius of 30 cm, the converted radius is 0.3 m, and the area becomes \( A_2 = \pi (0.3)^2 = 0.09\pi \text{ m}^2 \).

The area is crucial because it directly influences the magnetic dipole moment. Larger areas result in larger magnetic moments when the current is constant.

The net magnetic moment refers to the combined magnetic effect of a system of current-carrying loops. To understand this, we consider both the direction and magnitude of each loop's magnetic dipole moment.
In the exercise, both loops carry a clockwise current. This means their magnetic moments aid each other, contributing to a larger net magnetic moment. Mathematically, this is computed as:

• For the inner loop, \( \mu_1 = 7.00 \text{ A} \times 0.04\pi \text{ m}^2 = 0.28\pi \text{ Am}^2 \).
• For the outer loop, \( \mu_2 = 7.00 \text{ A} \times 0.09\pi \text{ m}^2 = 0.63\pi \text{ Am}^2 \).
• The total, or net, magnetic moment when currents are aligned is \( \mu_{net} = 0.28\pi + 0.63\pi = 0.91\pi \text{ Am}^2 \).

However, if one loop's current is reversed, its magnetic moment becomes negative, partially cancelling the effect of the other loop. Understanding how to calculate and appreciate this balance helps in many applications, from magnetic resonance imaging (MRI) to studying magnetic fields in physics.