30.8
ファラデーの法則
ファラデーの法則では、誘導起電力は単位時間あたりの磁束の負の変化であると述べています。 磁場の変化、または磁場に対するコイルの領域の向きの変化により、電圧 (emf) が誘導されます。 磁束は、特定の表面積を通る磁力線の数を測定します。 磁束は、磁場ベクトルと面積ベクトルの内積の積分から推定されます…
ファラデーの法則では、閉伝導ループでは、誘導された起電力は、そのループを通る磁束の負の時間微分に等しいとされています。誘導起電力の方向は、後にレンツによって与えられました。
導通ループがN個の同一の巻線で構成され、各巻を通過する磁束が同じである場合、総磁束は各巻を通る磁束のN倍になります。したがって、総誘導起電力はNに磁束の変化率を掛けたものになります。
長さ0.25メートルの正方形のコイルを考えてみましょう。これは、500ターンのワイヤーを密に巻いたものです。このコイルは、毎秒0.2テスラの速度で増加する磁場の中に置かれます。
次に、コイル内の誘導起電力の大きさは、ファラデーの法則を使用して計算できます。値を代入すると、誘導起電力の大きさを推定できます。
これらのパラメータのいずれかまたはそれらの組み合わせを変更することにより、起電力が誘発される可能性があることを観察することが重要です。
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Q1: What does Faraday's law state about induced emf in a conducting loop?
Faraday's law states that the induced emf in a closed conducting loop equals the negative time derivative of magnetic flux through that loop. This means the induced emf is directly proportional to how quickly the magnetic flux changes. The negative sign indicates the direction of the induced emf, which is determined by Lenz's law. Any change in the magnetic field or coil orientation induces a voltage.
Q2: How does the number of coil turns affect the total induced emf?
When a conducting loop consists of N identical turns with the same magnetic flux through each turn, the total magnetic flux is N times the flux through a single turn. Consequently, the total induced emf is N multiplied by the rate of change of magnetic flux. This relationship allows engineers to increase induced emf by adding more tightly wound turns to the coil.
Q3: What parameters can be changed to induce an emf in a coil?
An emf can be induced by changing the magnetic field strength, the orientation of the coil's area relative to the magnetic field, or a combination of both. For example, if a square coil is placed in an increasing magnetic field, the changing flux induces an emf. Similarly, rotating the coil changes the dot product of the magnetic field and area vectors, also inducing an emf.
Q4: How is magnetic flux calculated and what does it represent?
Magnetic flux measures the number of magnetic field lines passing through a given surface area. It is calculated as the integral of the dot product of the magnetic field vector and the area vector. This calculation accounts for both the field strength and the angle between the field and the surface. Understanding magnetic flux is essential for applying Faraday's law to real-world electromagnetic systems.
Q5: What are practical applications of Faraday's law in everyday devices?
Ground fault interrupter (GFI) devices use Faraday's law as a circuit breaker to prevent electrical shocks. Electric guitars employ the principle when a pick coil near a vibrating string detects changes in magnetic flux caused by the string's motion. This changing flux produces an emf that is amplified to create sound. These applications demonstrate how induced electric fields enable modern technology.
Q6: How would you calculate the induced emf in a specific coil using Faraday's law?
To calculate induced emf, substitute the known values into Faraday's law: emf equals negative N times the rate of change of magnetic flux. For a square coil with 500 turns and 0.25-meter sides in a magnetic field increasing at 0.2 tesla per second, multiply 500 by the area (0.0625 m²) and the field change rate to find the magnitude of induced emf.
Q7: Why is the negative sign important in Faraday's law?
The negative sign in Faraday's law describes the direction in which the induced emf drives current around a circuit, reflecting Lenz's law. This sign indicates that the induced current opposes the change in magnetic flux that created it. While the negative sign is mathematically important, the actual direction is most easily determined using Lenz's law as a practical guide.