⚡ Average EMF Induced in a Rectangular Wire Loop
📘 Question:
A rectangular loop with 120 turns and dimensions 0.3 m × 0.2 m is placed in a magnetic field that decreases from 1.2 T to 0.6 T in 0.18 s. What is the average emf induced in the loop?
✅ Step-by-Step Explanation:
🔹 Step 1: Given Values
- Number of turns, \( N = 120 \)
- Length = 0.3 m, Width = 0.2 m
- Initial magnetic field, \( B_i = 1.2\, \text{T} \)
- Final magnetic field, \( B_f = 0.6\, \text{T} \)
- Time interval, \( \Delta t = 0.18\, \text{s} \)
🔹 Step 2: Area of the Rectangular Loop
A = length × width = 0.3 × 0.2 = 0.06 m²
🔹 Step 3: Change in Magnetic Flux
ΔΦ = (B_f – B_i) × A = (0.6 – 1.2) × 0.06 = -0.036 Wb
🔹 Step 4: Use Faraday’s Law of Induction
EMFavg = |N × ΔΦ / Δt| = |120 × (-0.036) / 0.18| = 24.0 V
🎯 Final Answer:
The average induced EMF is 24.0 V.