91Ó°ÊÓ

A current loop is essentially a loop of wire through which an electric current flows. In this exercise, we have a single-turn square loop of wire. The current within the wire is important because it interacts with the magnetic field, producing a magnetic force. This loop can be visualized on a small scale like a rectangle cut out from a piece of aluminum foil. In our problem, the loop is laid flat on a tabletop.

Key characteristics of the current loop in this problem include:

• It carries a current, which is given as 18 amperes (A).
• Each side of the loop measures 15 cm, translating to 0.15 meters for calculation purposes.
• The loop is initially lying flat, meaning it does not experience significant forces until exposed to a magnetic field.

Current loops are significant in various applications, including electric motors and generators. They play a crucial role in producing magnetic fields and forces that can do work, just as in this exercise, where we find one side of the loop experiencing an upward lift when exposed to a magnetic field.

Magnetic force is the interaction that happens when a current-carrying wire is in the presence of a magnetic field. This phenomenon is the basis for the force affecting one side of the current loop in our exercise, causing it to tip.

Understanding magnetic force involves some key details:

• The magnitude of this magnetic force (\( F_{B} \)) can be calculated using the formula: \( F_{B} = I \times L \times B \), where \( I \) is the current, \( L \) is the length of the wire, and \( B \) is the magnetic field.
• For the loop to begin tipping, the magnetic force must create enough torque to overcome the gravitational hold on the loop, initially keeping it flat on the surface.

When one side of our loop experiences this force, it results in rotational motion. This is through the interaction of the current in the wire and the external magnetic field. As we calculated, the minimum magnetic field needed for this tipping to occur is about 0.1272 Tesla. Understanding this relationship is fundamental not just for physics, but also for engineering applications like designing electric motors.

Gravitational force acts as the opposing force in our problem. It helps to initially hold the loop flat against the tabletop. The loop's mass, along with the gravitational acceleration, dictates the strength of the gravitational pull.

Key points about gravitational force in this situation are:

• We calculate it using the formula \( F_g = m \times g \), where \( m \) is the mass of the loop (0.035 kg), and \( g \) stands for the acceleration due to gravity (approximately 9.81 m/s²).
• The resulting gravitational force is found to be 0.34335 Newtons, acting downward, opposing any upward movement of the loop.

The gravitational force also creates a torque about the pivot. This pivot point is the line along the edge of the loop that remains in contact with the table while tipping occurs. The battle between gravitational and magnetic torques determines whether the loop can tip up. Hence, comprehending how gravitational force interacts with the magnetic force explains why the minimum magnetic field must overcome this torque to start turning the loop.