⚡ Average EMF Induced in a Circular Loop
📘 Question:
A circular loop with 40 turns and a radius of 12 cm is placed in a magnetic field that increases from 0.2 T to 0.8 T in 0.25 s. Find the average emf induced in the loop.
✅ Step-by-Step Solution:
🔹 Step 1: Given Values
- Number of turns, \( N = 40 \)
- Radius, \( r = 12\, \text{cm} = 0.12\, \text{m} \)
- Initial magnetic field, \( B_i = 0.2\, \text{T} \)
- Final magnetic field, \( B_f = 0.8\, \text{T} \)
- Time interval, \( \Delta t = 0.25\, \text{s} \)
🔹 Step 2: Area of the Circular Loop
A = πr² = π × (0.12)² ≈ 0.0452 m²
🔹 Step 3: Change in Magnetic Flux
ΔΦ = (B_f – B_i) × A = (0.8 – 0.2) × 0.0452 = 0.0271 Wb
🔹 Step 4: Apply Faraday’s Law
EMFavg = |N × ΔΦ / Δt| = |40 × 0.0271 / 0.25| = 4.34 V
🎯 Final Answer:
The average induced EMF is 4.34 V.