Ch 30: Electromagnetic Induction

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796당신이 사용하는 게 아니라요?교과서 변경

Knight Calc 5th Edition

Ch 30: Electromagnetic Induction

문제 1

30장, 문제 1

The earth’s magnetic field strength is 5.0×10⁻⁵ T. How fast would you have to drive your car to create a 1.0 V motional emf along your 1.0-m-tall radio antenna? Assume that the motion of the antenna is perpendicular to $\vec{B}$ .

검증된 단계별 안내

Step 1: Understand the concept of motional emf. Motional emf is generated when a conductor moves through a magnetic field, and it is given by the formula:

ε = B l v

, where

ε

is the emf,

B

is the magnetic field strength,

l

is the length of the conductor, and

v

is the velocity of the conductor.

Step 2: Rearrange the formula to solve for velocity

v

. The formula becomes:

v = \frac{ε}{B l}

Step 3: Substitute the given values into the formula. The emf

ε

is 1.0 V, the magnetic field strength

B

5.0×10

⁻⁵ T, and the length of the antenna

l

is 1.0 m.

Step 4: Perform the substitution into the formula:

v = \frac{1.0}{5.0×10−5 \times 1.0}

. This will give the velocity required to generate the specified emf.

Step 5: Interpret the result. The calculated velocity will represent how fast the car must move perpendicular to the magnetic field to produce a motional emf of 1.0 V along the 1.0-m-tall antenna.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

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주요 개념

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

Motional Electromotive Force (emf)

Motional emf is generated when a conductor moves through a magnetic field, inducing a voltage across the conductor. The magnitude of the induced emf can be calculated using the formula emf = B * L * v, where B is the magnetic field strength, L is the length of the conductor, and v is the velocity of the conductor relative to the magnetic field.

Magnetic Field Strength

Magnetic field strength, measured in teslas (T), quantifies the intensity of a magnetic field. In this context, the Earth's magnetic field strength is given as 5.0×10^−5 T, which influences the amount of emf generated when a conductor moves through it. Understanding this value is crucial for calculating the required speed to achieve a specific emf.

Perpendicular Motion

When the motion of a conductor is perpendicular to the magnetic field lines, the induced emf is maximized. This is because the angle between the velocity vector of the conductor and the magnetic field vector is 90 degrees, leading to the most effective interaction. In this problem, the assumption that the antenna moves perpendicularly to the magnetic field is essential for applying the motional emf formula correctly.