What is the magnitude of the torque on the current loop in FIGURE EX29.39?

검증된 단계별 안내

Step 1: Identify the formula for torque on a current loop. The torque (τ) on a current loop in a magnetic field is given by τ = μ × B, where μ is the magnetic moment of the loop and B is the magnetic field.

Step 2: Calculate the magnetic moment (μ) of the loop. The magnetic moment is given by μ = I × A, where I is the current in the loop and A is the area of the loop. Use the dimensions provided in the figure to calculate the area (A = length × width).

Step 3: Determine the magnetic field (B) at the location of the loop. The magnetic field due to a long straight wire carrying current (I) is given by B = (μ₀ × I) / (2π × r), where μ₀ is the permeability of free space, I is the current in the wire, and r is the distance from the wire to the loop.

Step 4: Compute the torque (τ) using the values of μ and B. Ensure that the direction of the magnetic moment and the magnetic field are considered to calculate the cross product μ × B.

Step 5: Verify the units and ensure consistency in calculations. The torque should be expressed in Newton-meters (N·m).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Torque

Torque is a measure of the rotational force applied to an object, calculated as the product of the force and the distance from the pivot point (lever arm). It is a vector quantity, meaning it has both magnitude and direction, and is crucial in understanding how forces cause objects to rotate. The formula for torque (τ) is τ = r × F, where r is the distance from the pivot to the point of force application, and F is the force applied.

Magnetic Field

A magnetic field is a region around a magnetic material or a moving electric charge within which the force of magnetism acts. It is represented by magnetic field lines that indicate the direction and strength of the field. In the context of current-carrying loops, the magnetic field interacts with the current to produce torque, influencing the loop's orientation in the field.

Current Loop

A current loop is a closed loop of wire through which electric current flows. When placed in a magnetic field, the interaction between the magnetic field and the current generates a torque that can cause the loop to rotate. The magnitude of the torque depends on the current flowing through the loop, the area of the loop, and the strength of the magnetic field, making it essential for applications in electric motors and generators.