Induced Voltage in Alternating Fields?

📌 CONCEPT: Electromagnetic induction refers to the phenomenon where a changing magnetic field induces an electric field in a conductor, resulting in the generation of an electromotive force (EMF) or voltage.

📐 RULE / FORMULA: The induced voltage (ε) in a conductor placed in a changing magnetic field can be calculated using Faraday's law of electromagnetic induction, which states that ε = -N(dΦ/dt), where N is the number of turns of the conductor and Φ is the magnetic flux through the conductor.

💡 WORKED EXAMPLE: Consider a conductor with 100 turns placed in an alternating magnetic field with a frequency of 50 Hz. The magnetic field's amplitude remains constant at 10 mT. Using Faraday's law, we can calculate the induced voltage as ε = -N(dΦ/dt). Assuming the magnetic flux Φ varies sinusoidally with time, we can write dΦ/dt = 2πfΦm, where f is the frequency and Φm is the maximum magnetic flux. Substituting the values, we get ε = -100(2π(50)(10 × 10^(-3)))sin(2πft).

⚠️ COMMON MISTAKE: Students often confuse the direction of the induced voltage with the direction of the changing magnetic field, forgetting that the induced voltage is a result of the rate of change of the magnetic field.