Ch 28: Sources of Magnetic Field

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610당신이 사용하는 게 아니라요?교과서 변경

Young & Freedman Calc 14th Edition

Ch 28: Sources of Magnetic Field

문제 47b

28장, 문제 47b

A solenoid is designed to produce a magnetic field of 0.0270 T at its center. It has radius 1.40 cm and length 40.0 cm, and the wire can carry a maximum current of 12.0 A. What total length of wire is required?

검증된 단계별 안내

First, understand that the magnetic field inside a solenoid is given by the formula:

B = μ

₀nI, where

B

is the magnetic field,

μ

₀ is the permeability of free space,

n

is the number of turns per unit length, and

I

is the current.

Rearrange the formula to solve for

n

n = \frac{B}{μ}

₀I. Substitute the given values:

B = 0.0270

I = 12.0

A, and

μ

₀ = 4π × 10^-7 T·m/A.

Calculate the number of turns per unit length

n

using the rearranged formula.

Once

n

is found, calculate the total number of turns

N

by multiplying

n

by the length of the solenoid:

N = n × 0.40

Finally, calculate the total length of wire required by multiplying the number of turns

N

by the circumference of the solenoid:

L = N × 2π × 0.014

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.

Magnetic Field of a Solenoid

The magnetic field inside a solenoid is uniform and parallel to its axis, given by 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. Understanding this formula is crucial for calculating the required parameters of the solenoid.

Number of Turns in a Solenoid

The number of turns per unit length, n, is a key factor in determining the magnetic field strength of a solenoid. It is calculated as n = N/L, where N is the total number of turns and L is the length of the solenoid. This concept helps in understanding how the solenoid's design affects its magnetic properties.

Length of Wire in a Solenoid

The total length of wire required for a solenoid is determined by the number of turns and the circumference of the solenoid. It is calculated using the formula: total wire length = N × 2πr, where N is the number of turns and r is the radius of the solenoid. This concept is essential for solving the problem of wire length needed to achieve the desired magnetic field.