Section 5.4: Electromagnetic Induction
Electromagnetic induction is the process by which a changing magnetic field produces an electromotive force (EMF) in a conductor. This principle is the foundation of transformers, generators, and induction motors.
Induced EMF in a loop is proportional to the rate of change of magnetic flux:
where \( \Phi_B = B \cdot A \cdot \cos\theta \) is magnetic flux.
The direction of induced EMF opposes the change in magnetic flux that produced it, ensuring conservation of energy.
Example 1
A circular loop of area 0.05 m² is placed in a magnetic field changing at 0.2 T/s. Find the induced EMF.
\( \mathcal{E} = A \frac{dB}{dt} = 0.05 \cdot 0.2 = 0.01\ V \)
Example 2
A rod of length 0.5 m moves at 2 m/s perpendicular to a 0.3 T magnetic field. Determine EMF induced across its ends.
\( \mathcal{E} = B \cdot l \cdot v = 0.3 \cdot 0.5 \cdot 2 = 0.3\ V \)
Practice Problems
- A coil of 100 turns has area 0.02 m². Magnetic field decreases from 0.5 T to 0.1 T in 0.1 s. Find induced EMF.
- A straight conductor of 1 m moves at 5 m/s perpendicular to 0.4 T field. Compute EMF induced.
- Explain why Lenz's Law ensures energy conservation in induction.
- A rectangular loop rotates in a uniform magnetic field. Describe qualitatively how EMF varies with rotation.
- A generator produces 220 V at 50 Hz. If magnetic flux per turn is 0.02 Wb, estimate number of turns needed.