Edexcel A Level (IAL) Physics-4.30 Faraday & Lenz’s Law- Study Notes- New Syllabus
Edexcel A Level (IAL) Physics -4.30 Faraday & Lenz’s Law- Study Notes- New syllabus
Edexcel A Level (IAL) Physics -4.30 Faraday & Lenz’s Law- Study Notes -Edexcel A level Physics – per latest Syllabus.
Key Concepts:
- understand how to use Faraday’s law to determine the magnitude of an induced e.m.f. and be able to use the equation that combines Faraday’s and Lenz’s laws
\(\varepsilon=-\dfrac{d(N\phi)}{dt}\)
Faraday’s Law and Lenz’s Law of Electromagnetic Induction
Whenever the magnetic flux linkage through a coil changes, an e.m.f. is induced in the coil. The magnitude and direction of this induced e.m.f. are described by Faraday’s law and Lenz’s law.
Faraday’s Law of Electromagnetic Induction
Statement: The magnitude of the induced e.m.f. in a circuit is proportional to the rate of change of magnetic flux linkage.
\( \mathcal{E} \propto \dfrac{d(N\phi)}{dt} \)
This shows that:
- A greater change in flux linkage produces a larger e.m.f.
- A faster change in flux linkage produces a larger e.m.f.
- No change in flux linkage → no induced e.m.f.
Combining Faraday’s Law and Lenz’s Law
The complete mathematical expression is:
\( \mathcal{E} = -\dfrac{d(N\phi)}{dt} \)
- \( \mathcal{E} \) = induced e.m.f. (V)
- \( N \) = number of turns in the coil
- \( \phi \) = magnetic flux through one turn (Wb)
- \( t \) = time (s)
Meaning of the Minus Sign (Lenz’s Law)
The negative sign represents Lenz’s law.
Lenz’s law states: The induced e.m.f. is in a direction such that it opposes the change in magnetic flux that produces it.
- If flux is increasing, the induced e.m.f. acts to reduce it.
- If flux is decreasing, the induced e.m.f. acts to increase it.
- This ensures conservation of energy.
Determining the Magnitude of the Induced e.m.f.
To calculate the magnitude of the induced e.m.f.:
- Calculate the change in flux linkage \( \Delta(N\phi) \).
- Determine the time taken \( \Delta t \).
- Use:
\( \mathcal{E} = \left| \dfrac{\Delta(N\phi)}{\Delta t} \right| \)
The minus sign is used only to determine the direction, not the magnitude.
Ways to Change Magnetic Flux Linkage
- Move the magnet or the coil
- Change the speed of motion
- Change the strength of the magnetic field
- Change the area of the coil
- Rotate the coil
- Change the current in a nearby coil
Units
- Magnetic flux \( \phi \): weber (Wb)
- Flux linkage \( N\phi \): weber-turns (Wb)
- Induced e.m.f. \( \mathcal{E} \): volt (V)
Example (Easy)
The magnetic flux through a single-turn coil changes from \( 2.0\times10^{-3}\ \mathrm{Wb} \) to zero in \( 0.10\ \mathrm{s} \). Calculate the magnitude of the induced e.m.f.
▶️ Answer / Explanation
\( \Delta(N\phi) = 2.0\times10^{-3} \)
\( \mathcal{E} = \dfrac{2.0\times10^{-3}}{0.10} = 2.0\times10^{-2}\ \mathrm{V} \)
Example (Medium)
A coil of 200 turns experiences a change in magnetic flux per turn of \( 5.0\times10^{-5}\ \mathrm{Wb} \) in \( 0.020\ \mathrm{s} \). Calculate the induced e.m.f.
▶️ Answer / Explanation
\( \Delta(N\phi) = 200 \times 5.0\times10^{-5} = 1.0\times10^{-2}\ \mathrm{Wb} \)
\( \mathcal{E} = \dfrac{1.0\times10^{-2}}{0.020} = 0.50\ \mathrm{V} \)
Example (Hard)
Explain why the induced current always opposes the motion producing it.
▶️ Answer / Explanation
- An opposing current creates an opposing magnetic field.
- This resists the change in magnetic flux.
- Energy must be supplied to maintain the motion.
- This is consistent with conservation of energy.