A solenoid 25.0 cm long and with a cross-sectional area of 0.500 cm² contains 400 turns of wire and carries a current of 80.0 A. Calculate: the total energy contained in the coil's magnetic field (assume the field is uniform);

검증된 단계별 안내

First, understand that the energy stored in the magnetic field of a solenoid can be calculated using the formula for the energy density of a magnetic field: \( u = \frac{1}{2} \frac{B^2}{\mu_0} \), where \( B \) is the magnetic field and \( \mu_0 \) is the permeability of free space.

Calculate the magnetic field \( B \) inside the solenoid using the formula \( B = \mu_0 n I \), where \( n \) is the number of turns per unit length (\( n = \frac{N}{L} \)), \( N \) is the total number of turns, \( L \) is the length of the solenoid, and \( I \) is the current.

Substitute the values into the formula for \( n \): \( n = \frac{400}{0.25} \) turns/m. Then calculate \( B \) using \( B = \mu_0 n I \).

Once \( B \) is calculated, find the energy density \( u \) using \( u = \frac{1}{2} \frac{B^2}{\mu_0} \).

Finally, calculate the total energy stored in the solenoid by multiplying the energy density \( u \) by the volume of the solenoid: \( E = u \times \text{Volume} \), where the volume is \( A \times L \) and \( A \) is the cross-sectional area.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

10m

도움이 되었나요?

주요 개념

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

Magnetic Field in a Solenoid

The magnetic field inside a long solenoid is uniform and can be calculated using the formula B = μ₀nI, where B is the magnetic field, μ₀ is the permeability of free space, n is the number of turns per unit length, and I is the current. This concept is crucial for understanding how the solenoid generates a magnetic field.

Magnetic Energy Density

Magnetic energy density is the energy stored per unit volume in a magnetic field, given by the formula u = B²/(2μ₀), where u is the energy density, B is the magnetic field, and μ₀ is the permeability of free space. This concept helps in determining how much energy is stored in the magnetic field of the solenoid.

Total Magnetic Energy in a Solenoid

The total energy stored in the magnetic field of a solenoid can be calculated by multiplying the magnetic energy density by the volume of the solenoid. The volume is found by multiplying the cross-sectional area by the length of the solenoid. This concept is essential for calculating the total energy contained in the solenoid's magnetic field.