Induced EMF in a Rotating Coil?

📌 CONCEPT: Electromagnetic induction is the production of an electromotive force (EMF) across a conductor by a changing magnetic field, without the need for a physical connection to a power source.

📐 RULE / FORMULA: The average induced EMF in a rotating coil is given by the formula ε = (N × A × ω) × (B × r × sin(θ)), where ε is the induced EMF, N is the number of turns, A is the area of the coil, ω is the angular speed, B is the magnetic field strength, r is the radius of the coil, and θ is the angle between the coil's normal and the magnetic field.

💡 WORKED EXAMPLE: A coil of radius 20 cm with 100 turns is rotated at 50 revolutions in 20 seconds in a uniform magnetic field of 0.2 T. The average induced EMF in the coil can be calculated as follows: first, we find the angular speed ω = (50 × 2×π) / 20 = 5.02 rad/s. Then, we use the formula ε = (N × A × ω) × (B × r × sin(90°)) = 100 × (0.2 m)^2 × 5.02 rad/s × 0.2 T × 0.1 m × 1 = 1.01 V.

⚠️ COMMON MISTAKE: Students often forget to include the angle θ in the formula, which is critical for determining the correct direction of the induced EMF. They may also neglect to convert the number of revolutions to angular speed, which can lead to incorrect results.