Section 5.4: Induction & Generators
Induction occurs when a changing magnetic flux induces an electromotive force (emf). Generators convert mechanical energy into electrical energy using electromagnetic induction.
- Induced EMF in a Coil: \[ \mathcal{E} = -N \frac{d\Phi_B}{dt} \] where \(N\) = number of turns.
- AC Generator: A rotating coil in a magnetic field produces alternating emf: \[ \mathcal{E} = NBA \omega \sin(\omega t) \]
- Applications include electric power generation and induction devices.
Example: EMF in a Generator
A coil with 100 turns, area 0.01 m² rotates in a 0.5 T field at 50 rad/s. Find the maximum induced emf.
\[ \mathcal{E}_{max} = N B A \omega = 100 \times 0.5 \times 0.01 \times 50 = 2.5 \, \text{V} \]
Practice Problems
- A coil of 50 turns and area 0.02 m² rotates in a 0.3 T magnetic field at 60 rad/s. Calculate the maximum emf.
- Explain why the induced current in a generator is alternating.
- Describe how changing the number of turns affects the induced emf.
- Give two real-life applications of electromagnetic induction.
- A coil experiences a magnetic flux change of 0.05 Wb in 0.1 s. If it has 10 turns, calculate the induced emf.