To find the induced electromotive force (emf) in the coil when it is rotated in a magnetic field, we can use Faraday's law of electromagnetic induction. This law states that the induced emf in a circuit is equal to the rate of change of magnetic flux through the circuit. Let's break down the problem step by step.
Understanding the Components
We have the following information:
- Magnetic field strength (B) = 6 x 10-5 W/m2
- Area of the coil (A) = 0.05 m2
- Number of turns (N) = 1500
- Angle of rotation (θ) = 90 degrees
- Time taken for rotation (Δt) = 0.1 s
Calculating the Initial and Final Magnetic Flux
The magnetic flux (Φ) through the coil is given by the formula:
Φ = B × A × cos(θ)
Initially, when the coil is perpendicular to the magnetic field, θ = 0 degrees. Therefore:
Φinitial = B × A × cos(0) = B × A = (6 x 10-5) × (0.05) = 3 x 10-6 Wb (Webers)
After rotating the coil by 90 degrees, the angle θ becomes 90 degrees. Thus:
Φfinal = B × A × cos(90) = B × A × 0 = 0 Wb
Finding the Change in Magnetic Flux
The change in magnetic flux (ΔΦ) is calculated as:
ΔΦ = Φfinal - Φinitial = 0 - (3 x 10-6) = -3 x 10-6 Wb
Applying Faraday's Law
According to Faraday's law, the induced emf (ε) can be calculated using the formula:
ε = -N × (ΔΦ/Δt)
Substituting the values we have:
ε = -1500 × (-3 x 10-6 Wb) / (0.1 s)
ε = 1500 × (3 x 10-6) / (0.1) = 1500 × 3 x 10-5
ε = 4.5 x 10-2 V
Final Result
The induced emf in the coil when it is rotated 90 degrees in the magnetic field is 0.045 V, or 45 mV. This demonstrates how a change in orientation within a magnetic field can generate an electric potential, a fundamental principle in electromagnetism.
