Induction in a Coiled Wire?

📌 CONCEPT: The phenomenon of electromagnetic induction occurs when a conductor, such as a coiled wire, experiences a change in its magnetic field, resulting in the generation of an electromotive force (emf).

📐 RULE / FORMULA: According to Faraday's law of electromagnetic induction, the induced emf (ε) in a coil is directly proportional to the rate of change of the magnetic flux (Φ) through the coil, given by the equation ε = -N(dΦ/dt), where N is the number of turns in the coil.

💡 WORKED EXAMPLE: When the magnetic field is reduced by a factor of two in a time period of 1 second, the change in magnetic flux is Φ = B*A, where B is the magnetic field strength and A is the area of the coil. Since the radius of the coil is increased by 20%, the area of the coil increases by a factor of 1.2^2 = 1.44. Therefore, the induced emf is ε = -N(dΦ/dt) = -N*B*A*(2/1 - 1/1) * 1.44, which increases by a factor of 2.88.

⚠️ COMMON MISTAKE: Students often forget to consider the change in the magnetic flux due to the increase in the coil's radius, which affects the induced emf.