Question
Obtain Faraday's law of induction explaining Faraday's experiments regarding electric induction with reference to magnetic flux.
✓
Answer
→From experimental observations of experiments of Faraday and Henry, it is clear that initially magnetic flux gets linked with coil, after that linked magnetic flux changes and then induced current or induced emf arises.
•Experiment 1 :
→In experiment of coil and magnet, magnetic flux is linked with coil due to magnet.
→On giving relative motion between them, linked magnetic flux changes and induced current arises.
• Experiment 2 :
→In experiment of two coils, on passing electric current through any one coil, magnetic field is produced. Due to this, magnetic flux is linked with other coil.
→On giving relative motion between two coils, linked magnetic flux changes and induced current is produced.
• Experiment 3 :
→In experiment of two stationary coils, making key on-off, produces magnetic field and hence magnetic flux linked with other coil changes and thus galvanometer shows deflection.
→ Keeping key in closed situation, linked magnetic flux does not change and galvanometer shows zero deflection.
→Thus, clear conclusion from all these experiments is that linking magnetic flux with coil by any means, changing linked magnetic flux with time, induced emf is produced.
• Faraday's law of electromagnetic induction :
→The magnitude of induced emf in a circuit is equal to the time rate of change of magnetic flux through the circuit.
→Induced emf is shown mathematically as below :
$\varepsilon=-\frac{d \phi_{ B }}{d t}$
→The negative sign in the equation indicates the direction of $\varepsilon$ and hence the direction of current in the closed circuit (loop). (It can also be said that it shows presence of Lenz's law.)
→ If number of turns in coil is N then
$\varepsilon=- N \frac{d \phi_{ B }}{d t}$
•Experiment 1 :
→In experiment of coil and magnet, magnetic flux is linked with coil due to magnet.
→On giving relative motion between them, linked magnetic flux changes and induced current arises.
• Experiment 2 :
→In experiment of two coils, on passing electric current through any one coil, magnetic field is produced. Due to this, magnetic flux is linked with other coil.
→On giving relative motion between two coils, linked magnetic flux changes and induced current is produced.
• Experiment 3 :
→In experiment of two stationary coils, making key on-off, produces magnetic field and hence magnetic flux linked with other coil changes and thus galvanometer shows deflection.
→ Keeping key in closed situation, linked magnetic flux does not change and galvanometer shows zero deflection.
→Thus, clear conclusion from all these experiments is that linking magnetic flux with coil by any means, changing linked magnetic flux with time, induced emf is produced.
• Faraday's law of electromagnetic induction :
→The magnitude of induced emf in a circuit is equal to the time rate of change of magnetic flux through the circuit.
→Induced emf is shown mathematically as below :
$\varepsilon=-\frac{d \phi_{ B }}{d t}$
→The negative sign in the equation indicates the direction of $\varepsilon$ and hence the direction of current in the closed circuit (loop). (It can also be said that it shows presence of Lenz's law.)
→ If number of turns in coil is N then
$\varepsilon=- N \frac{d \phi_{ B }}{d t}$
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