Section 5.3: Faraday’s Law
Faraday’s Law of Electromagnetic Induction states that a changing magnetic flux through a circuit induces an electromotive force (emf) in the circuit.
- Faraday’s Law: \[ \mathcal{E} = -\frac{d\Phi_B}{dt} \] where \( \Phi_B = B \cdot A \cdot \cos\theta \) is magnetic flux.
- Lenz’s Law: The induced emf generates a current whose magnetic field opposes the change in flux.
- Applications: generators, transformers, inductors, and electric motors.
Example: Induced EMF in a Loop
A circular loop of radius 0.1 m is in a magnetic field decreasing at 0.5 T/s. Find the induced emf.
\[ \Phi_B = B \cdot A = B \cdot \pi r^2 \Rightarrow \mathcal{E} = -\frac{d\Phi_B}{dt} = \pi (0.1)^2 (0.5) \approx 0.0157 \, \text{V} \]
Practice Problems
- A rectangular loop of area 0.2 m² experiences a magnetic field change of 0.8 T in 0.4 s. Calculate the induced emf.
- Explain qualitatively how Lenz’s Law ensures energy conservation.
- A coil of 50 turns has a changing magnetic flux of 0.03 Wb. Find the induced emf.
- Describe one real-life application of Faraday’s Law in everyday devices.
- A circular loop is rotated in a uniform magnetic field. Derive the expression for maximum induced emf.