What is the magnitude of the magnetic flux through the loop shown in FIGURE EX30.5?

검증된 단계별 안내

Step 1: Understand the concept of magnetic flux. Magnetic flux (Φ) is given by the formula Φ = B × A × cos(θ), where B is the magnetic field strength, A is the area through which the field passes, and θ is the angle between the magnetic field and the normal to the surface. In this case, the field is perpendicular to the loop, so cos(θ) = 1.

Step 2: Divide the loop into two regions based on the magnetic field strength. The left region has a magnetic field of 2.0 T, and the right region has a magnetic field of 1.0 T. Calculate the area of each region separately.

Step 3: Calculate the area of the left region. The width of the left region is 20 cm (0.20 m), and the height is 30 cm (0.30 m). Use the formula for area: A = width × height. For the left region, A_left = 0.20 m × 0.30 m.

Step 4: Calculate the area of the right region. The width of the right region is 40 cm (0.40 m), and the height is 30 cm (0.30 m). Use the formula for area: A = width × height. For the right region, A_right = 0.40 m × 0.30 m.

Step 5: Compute the magnetic flux for each region separately using Φ = B × A. For the left region, Φ_left = 2.0 T × A_left. For the right region, Φ_right = 1.0 T × A_right. Add the two fluxes together to find the total magnetic flux through the loop: Φ_total = Φ_left + Φ_right.

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

주요 개념

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

Magnetic Flux

Magnetic flux is a measure of the quantity of magnetism, taking into account the strength and extent of a magnetic field. It is defined as the product of the magnetic field (B) and the area (A) through which the field lines pass, and is given by the formula Φ = B · A · cos(θ), where θ is the angle between the magnetic field lines and the normal to the surface. The unit of magnetic flux is the Weber (Wb).

Magnetic Field Strength

Magnetic field strength, denoted as B, is a vector quantity that represents the intensity of a magnetic field at a given point in space. It is measured in teslas (T) and indicates the force experienced by a unit magnetic pole placed in the field. In the context of the question, different regions of the magnetic field are indicated with varying strengths (1.0 T and 2.0 T), which will affect the total magnetic flux through the loop.

Area of the Loop

The area of the loop is crucial for calculating magnetic flux, as it determines how much of the magnetic field lines pass through the loop. The area (A) can be calculated using the formula A = length × width. In this case, the dimensions of the loop are given as 20 cm by 40 cm, which must be converted to meters for consistency in SI units when calculating the magnetic flux.