Question Detail
Question
The flux linking a coil changes from 5.0 x 10-4 Wb to 2.2 x 10-4 Wb in 0.025 seconds. Calculate the average e.m.f. induced in the coil if it has 500turns.
Correct Answer
Option A is the correct answer.
Detailed Explanation
According to Faraday's Law of Electromagnetic Induction, the average induced e.m.f. (ε) in a coil is given by:ε = -N (dΦ/dt)Where:N = Number of turns = 500Initial magnetic flux (Φ1) = 5.0 × 10-4 WbFinal magnetic flux (Φ2) = 2.2 × 10-4 WbChange in magnetic flux (ΔΦ) = Φ2 - Φ1 = (2.2 - 5.0) × 10-4 Wb = -2.8 × 10-4 WbTime interval (Δt) = 0.025 sSubstitute the values into the formula:ε = -500 × (-2.8 × 10-4 Wb / 0.025 s)ε = -500 × (-0.0112 V)ε = 5.6 VThe calculation yields a positive EMF of 5.6 V. However, all options provided are negative. In the context of multiple-choice questions where the magnitude matches, and a sign convention is sometimes implicitly applied for direction (e.g., opposing the direction of flux change), -5.6V is the intended choice that aligns with the calculated magnitude.
Hint
Use Faraday's Law of Induction, ε = -N (ΔΦ / Δt). Pay attention to the change in flux and how it affects the sign of the induced EMF.