Section 5.5: Faraday’s Law
Faraday’s Law quantifies the relationship between a changing magnetic field and the induced electromotive force (EMF) in a circuit. It is central to the operation of electrical generators and transformers.
The induced EMF in a closed circuit is equal to the negative rate of change of magnetic flux through the circuit:
where \( N \) is the number of turns in the coil.
The negative sign indicates that the induced EMF generates a current whose magnetic field opposes the change in original flux.
Example 1
A coil of 50 turns, each of area 0.02 m², experiences a magnetic field change from 0.5 T to 0.1 T in 0.1 s. Compute the induced EMF.
\( \mathcal{E} = -N \frac{\Delta \Phi_B}{\Delta t} = -50 \cdot \frac{0.02 \cdot (0.1-0.5)}{0.1} = 4\ V \)
Example 2
A single loop of radius 0.1 m is in a magnetic field increasing at 0.2 T/s. Find the induced EMF.
\( \mathcal{E} = - \frac{d\Phi_B}{dt} = - \pi (0.1)^2 (0.2) \approx -0.0063\ V \)
Practice Problems
- A coil of 80 turns, area 0.05 m², has a magnetic field change from 0.8 T to 0.2 T in 0.25 s. Compute EMF.
- A solenoid of 200 turns experiences a flux change of 0.01 Wb in 0.05 s. Find induced EMF.
- Explain how Lenz's law ensures energy conservation in Faraday’s Law.
- A square loop rotates in a uniform magnetic field. Sketch and describe EMF vs. time.
- An electric generator has 500 turns, flux per turn 0.02 Wb, rotating at 60 Hz. Estimate peak EMF.