Faraday's Law of Electromagnetic Induction
Faraday's law states that the magnitude of induced emf in a circuit is equal to the rate of change of magnetic flux linked with the circuit. Mathematically, epsilon = - dPhiB/dt for one turn and epsilon = -N dPhiB/dt for N turns.
In one line: Faraday tells how much emf is induced from changing flux; the faster the flux changes and the more turns the coil has, the larger the emf. Remember: change in flux creates emf, rate of change sets its size, and Lenz's law sets its direction.
Concept Practice Coming SoonUnderstand it
An emf is induced whenever magnetic flux linked with a closed circuit changes with time. The change may happen by changing magnetic field, area, orientation, or by relative motion between a magnet and coil. The negative sign shows the direction given by Lenz's law.
Example
Formula and rule
Formula: epsilon = -N dPhiB/dt.
Here epsilon is induced emf in volt (V), N is the number of turns in the coil, PhiB is magnetic flux through one turn in weber (Wb), t is time in second (s), and dPhiB/dt is the rate of change of flux.
The minus sign represents Lenz's law: the induced emf acts in the direction that opposes the change in flux.
For magnitude in numericals, use |epsilon| = N |Delta PhiB|/Delta t.
See it worked out
Follow the example line by line, then use the same method on new questions.
Worked example
A coil of 200 turns has flux through each turn changing from 3.0 × 10−4 Wb to 1.0 × 10−4 Wb in 0.02 s.
- 1Magnitude of induced emf = N |Delta Phi|/Delta t = 200 x |1.0 × 10−4 - 3.0 × 10−4| / 0.02 = 200 × 2.0 × 10−4 / 0.02 = 2.0 V.
- 2The emf is produced because flux decreases rapidly.
Method you can reuse
- 1Find initial and final flux per turn.
- 2Calculate Delta Phi and time interval.
- 3Multiply by number of turns.
- 4Use magnitude for numerical value, then use Lenz's law if direction is asked.
Sketch it in your answer
Draw a coil connected to a galvanometer and a bar magnet moving toward or away from it. Label N and S poles, direction of motion, coil, galvanometer, and induced current direction for the chosen case.
Check yourself
Answer the question in your head before opening the answer.
Try it yourself
Why is no emf induced in a coil placed near a stationary magnet?
Think first, then show answerHide answer
Common wrong answer
Ignoring number of turns N or using final flux divided by time instead of change in flux divided by time.
Don't mix this up
Exam tip
Write it in the exam
Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.
How CBSE asks it
- 1
Enough for 1 mark
Faraday's law states that the magnitude of induced emf in a circuit is equal to the rate of change of magnetic flux linked with the circuit. Mathematically, epsilon = - dPhiB/dt for one turn and epsilon = -N dPhiB/dt for N turns.
- 2
Add for 2 marks
Example: When a bar magnet is pushed towards a coil connected to a galvanometer, the changing flux through the coil produces an induced emf and the galvanometer deflects.
- 3
Add for 3 marks
An emf is induced whenever magnetic flux linked with a closed circuit changes with time.
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