Induction in a Moving Coil?

📌 CONCEPT: Electromagnetic induction occurs when a conductor, such as a coil, moves through a magnetic field, resulting in an electromotive force (emf) being induced in the coil.

📐 RULE / FORMULA: The induced emf (ε) in a conductor is given by the equation ε = -N(dΦ/dt), where N is the number of turns of the coil, Φ is the magnetic flux, and t is time. However, in this case, we are dealing with a changing magnetic field due to the motion of the coil, so we use the equation ε = -N(dΦ/dB)(dB/dt).

💡 WORKED EXAMPLE: Suppose the rotation speed of the disc is doubled from 10 rad/s to 20 rad/s. If the magnetic field (B) is uniform and the area of the coil is constant, the change in magnetic flux (dΦ) is directly proportional to the angular speed (ω = dθ/dt). Since the angular speed is doubled, the change in magnetic flux is also doubled, resulting in a doubling of the induced emf. However, if the magnetic field is not uniform, the induced emf may not double.

⚠️ COMMON MISTAKE: Students often assume that the induced emf will always double when the rotation speed of the disc is doubled, without considering the factors that influence the magnetic flux, such as the uniformity of the magnetic field or the geometry of the coil.