Physics Problem: Induced EMF in a Rectangular Wire Loop
Question
A rectangular loop of wire with sides 0.137 m and 0.537 m lies in a plane perpendicular to a constant magnetic field. The magnetic field has a magnitude of 0.522 T and is directed parallel to the normal of the loop’s surface. In a time of 0.210 s, what is the average emf induced in the loop?
Answer
📘 Concept Used – Faraday’s Law of Electromagnetic Induction
Faraday’s Law is used to calculate the average induced emf:
emfavg = |ΔΦ / Δt|
where Φ = B × A
where Φ = B × A
- B = magnetic field strength (in T)
- A = area of the loop (in m²)
- Δt = time interval (in seconds)
🧾 Given Values
- Magnetic field, B = 0.522 T
- Dimensions of the loop: 0.137 m × 0.537 m
- Time interval, Δt = 0.210 s
🧮 Step-by-Step Calculation
Step 1: Area of the loop
A = 0.137 × 0.537 = 0.073509 m²
Step 2: Change in magnetic flux
ΔΦ = B × A = 0.522 × 0.073509 = 0.038403 Wb
Step 3: Calculate the average induced emf
emfavg = 0.038403 / 0.210 = 0.183 V
✅ Final Answer
0.183 V