Physics Class 12 Part I…
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Faradays Experiments Flux

🎓 Class 12 Physics CBSE Theory Ch 6 – Electromagnetic Induction ⏱ ~14 min
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આ MCQ મોડ્યુલ આના પર આધારિત છે: Faradays Experiments Flux

આ મૂલ્યાંકન આના પર આધારિત હશે: Faradays Experiments Flux

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Faradays Experiments Flux

6.1 Introduction

In 1820, Hans Christian Oersted observed that an electric current produces a magnetic field. The natural follow-up question - can a magnetic field produce an electric current? - took eleven more years to settle. In 1831, Michael Faraday in England (and almost simultaneously Joseph Henry in America) showed that a changing magnetic field induces an electric current. This phenomenon, called electromagnetic induction (EMI), is the basis of nearly every electrical generator and transformer in use today.

6.2 The Experiments of Faraday and Henry

6.2.1 Experiment 1 - Bar magnet and a coil

A coil is connected to a sensitive galvanometer. When a bar magnet is moved toward the coil, the galvanometer needle deflects briefly. When the magnet is moved away, the needle deflects in the opposite direction. When the magnet is held stationary - even close to the coil - the galvanometer reads zero.

Coil N S v G
Fig 6.1 Faraday's first experiment - moving the bar magnet relative to the coil deflects the galvanometer.

6.2.2 Experiment 2 - Two coils

A primary coil P (carrying current I from a battery via a switch) sits coaxially inside a secondary coil S connected to a galvanometer. When the switch is opened or closed, or the current in P is varied with a rheostat, the galvanometer in S deflects briefly. A steady current in P produces no deflection.

6.2.3 Faraday's qualitative conclusion

In every case, an EMF (and hence current) appears in the secondary circuit only while the magnetic flux linked with it is changing. The change of flux is the cause; relative motion, varying current, or rotation are merely ways of producing such a change.

6.3 Magnetic Flux

Magnetic flux through any surface bounded by a closed circuit is

\[\Phi_B = \int_S \vec B \cdot d\vec A\]

For a uniform field B over a flat area A:

\[\Phi_B = BA\cos\theta\]

where θ is the angle between B and the area normal. SI unit: weber (Wb) = T·m².

n̂ B θ
Fig 6.2 ΦB = B A cos θ where θ is the angle between B and area normal n̂.

6.4 Faraday's Law of Induction

Faraday's law: The EMF induced in a closed circuit equals the negative rate of change of magnetic flux through any surface bounded by the circuit.
\[\varepsilon = -\dfrac{d\Phi_B}{dt}\]
For a coil of N tightly wound turns, the flux through each turn adds, and the EMF is multiplied:
\[\varepsilon = -N\dfrac{d\Phi_B}{dt}\]
The negative sign anticipates the direction (Lenz's law), discussed in Part 2.

Since Φ = BA cos θ, the flux can change in three ways:

  1. B varies in time (e.g. switch off/on a primary coil current).
  2. A varies in time (e.g. expand/contract a loop, or move a slider on a U-rail).
  3. θ varies in time (e.g. rotate the coil in a generator).

Worked Example 6.1 - Flux through a tilted loop

Example 6.1 L3 Apply

A circular loop of radius 5.0 cm is placed in a uniform magnetic field B = 0.20 T. Find the flux when (a) the loop's plane is perpendicular to B, (b) the plane is parallel to B, (c) the normal makes 60° with B.

A = πr² = π(0.05)² = 7.85 × 10⁻³ m².

(a) Plane ⊥ B ⇒ θ = 0; Φ = BA = 0.20 × 7.85 × 10⁻³ = 1.57 × 10⁻³ Wb.

(b) Plane ∥ B ⇒ θ = 90°; Φ = 0.

(c) Φ = BA cos 60° = 1.57 × 10⁻³ × 0.5 = 7.85 × 10⁻⁴ Wb.

Worked Example 6.2 - EMF from a flux change

Example 6.2 L3 Apply

The flux through a 200-turn coil decreases from 0.10 Wb to 0.04 Wb in 0.50 s. Find the average induced EMF.

ΔΦ = 0.04 − 0.10 = −0.06 Wb; Δt = 0.50 s.

|ε| = N |ΔΦ/Δt| = 200 × (0.06/0.50) = 200 × 0.12 = 24 V.

Worked Example 6.3 - Coil rotated through 90°

Example 6.3 L4 Analyse

A 50-turn coil of area 100 cm² lies with its plane perpendicular to a 0.30 T field. The coil is flipped through 90° in 0.10 s. Find the EMF.

Initial Φ per turn = BA cos 0° = 0.30 × 100 × 10⁻⁴ = 3.0 × 10⁻³ Wb.

Final Φ = BA cos 90° = 0.

|ε| = N × ΔΦ/Δt = 50 × 3.0 × 10⁻³/0.10 = 1.5 V.

Interactive: Flux Change Calculator L3 Apply

Adjust B, A, angle θ and time Δt to predict the magnitude of the induced EMF.

ΔΦ per turn = 0.0030 Wb  |  |ε| = 1.50 V
Activity 6.1 - Bar magnet, coil and galvanometerL4 Analyse
  1. Make a 50-turn coil of insulated copper wire, ~5 cm in diameter.
  2. Connect it to a sensitive (centre-zero) galvanometer.
  3. Push a bar magnet quickly into the coil; pull it out quickly; hold it stationary inside.
Predict: How does the deflection (sign and size) depend on the speed of motion? On the orientation of the magnet?

Faster motion ⇒ greater dΦ/dt ⇒ larger deflection. Reversing the magnet swaps the sign of the deflection. Stationary magnet ⇒ no deflection (no flux change). The relationship is exactly ε = −N dΦ/dt.

Competency-Based Questions L1-L6

A 100-turn coil of area 50 cm² is placed in a magnetic field that varies uniformly from 0.10 T to 0.50 T in 0.20 s, perpendicular to its plane.
1. The change in flux per turn is: L3 Apply
  • (a) 5.0 × 10⁻⁴ Wb
  • (b) 2.0 × 10⁻³ Wb
  • (c) 0.20 Wb
  • (d) 2.0 × 10⁻⁴ Wb
(b) ΔΦ = ΔB × A = 0.40 × 50 × 10⁻⁴ = 2.0 × 10⁻³ Wb.
2. The induced EMF in the coil is: L3 Apply
  • (a) 0.20 V
  • (b) 0.10 V
  • (c) 1.0 V
  • (d) 2.0 V
(c) ε = N(ΔΦ/Δt) = 100 × 2.0 × 10⁻³/0.20 = 1.0 V.
3. State Faraday's law of electromagnetic induction. L1 Remember
The EMF induced in a closed loop equals the negative rate of change of magnetic flux linked with it: ε = −dΦB/dt (or −N dΦB/dt for an N-turn coil).
4. List three distinct ways to change the flux through a stationary coil. L4 Analyse
(i) Vary B in time (e.g. switch the current of a primary coil). (ii) Change the angle θ between B and the area normal (rotate the coil). (iii) Change the area A enclosed (deform the loop, slide a movable conductor on a U-rail).
5. A student claims "if a coil is in a magnetic field, an EMF must appear in it". Critique. L5 Evaluate
The claim is incorrect. EMF appears only if the flux is changing. A stationary coil in a steady field has zero EMF, no matter how strong the field. Faraday's law links EMF to dΦ/dt, not to Φ itself.

Assertion-Reason Pairs L4 Analyse

Options: (A) Both true, R correct explanation. (B) Both true, R not the explanation. (C) A true, R false. (D) A false, R true.

Assertion: The faster a magnet is moved into a coil, the larger the induced EMF.
Reason: Faster motion ⇒ greater dΦ/dt.
(A). Reason directly explains the assertion.
Assertion: A stationary coil in a uniform but changing field experiences an EMF.
Reason: The flux through the coil changes because B changes.
(A). Both true; reason explains the assertion.
Assertion: The SI unit of magnetic flux is the volt.
Reason: EMF = dΦ/dt has units of V.
(D). Assertion is false: the SI unit of Φ is the weber (Wb = V·s), not the volt. Reason is true.

Frequently Asked Questions - Faradays Experiments Flux

What is the main concept covered in Faradays Experiments Flux?
In NCERT Class 12 Physics Chapter 6 (Electromagnetic Induction), "Faradays Experiments Flux" covers the core principles and equations students need for board exam success. The MyAiSchool lesson explains the topic with definitions, derivations, worked examples, and interactive simulations. Key formulas and dimensional analysis are included to build conceptual depth and problem-solving skills aligned with the CBSE 2025-26 syllabus.
How is Faradays Experiments Flux useful in real-life applications?
Real-life applications of "Faradays Experiments Flux" from NCERT Class 12 Physics Chapter 6 include electronics, communication systems, medical imaging, solar energy, semiconductor devices, and modern technology. The MyAiSchool lesson links every concept to a tangible example so students see physics as a problem-solving framework for the physical world, not as abstract formulas.
What are the key formulas in Faradays Experiments Flux?
Key formulas in "Faradays Experiments Flux" (NCERT Class 12 Physics Chapter 6 Electromagnetic Induction) are derived step-by-step in the MyAiSchool lesson. Students should memorize the final formula AND understand its derivation for full board marks. Each formula is listed with its dimensional formula, SI unit, applicability range, and common pitfalls. The Summary section at the end of each part includes a quick-reference formula card.
How does this part connect to other parts of Chapter 6?
NCERT Class 12 Physics Chapter 6 (Electromagnetic Induction) is structured so each part builds on the previous one. "Faradays Experiments Flux" connects directly to neighbouring parts via shared definitions, units, and methodology. The MyAiSchool lesson cross-references related concepts with internal links so students can navigate the whole chapter as one connected story rather than disconnected fragments.
What types of CBSE board questions come from Faradays Experiments Flux?
CBSE board questions from "Faradays Experiments Flux" typically include: (1) 1-mark MCQs on definitions and formulas, (2) 2-mark short-answer derivations or applications, (3) 3-mark numerical problems with units, (4) 5-mark long-answer derivations followed by application. The MyAiSchool lesson tags each Competency-Based Question (CBQ) with Bloom level (L1-L6) so students know how to study for each weight.
How can students use the interactive simulation effectively?
The interactive simulation in the "Faradays Experiments Flux" lesson allows students to adjust input parameters (sliders or selectors) and see physical quantities update in real time. To use it effectively: (1) try extreme values to understand limiting cases, (2) compare with the analytical formula, (3) check unit consistency, (4) test special configurations from worked examples. The simulation reinforces conceptual intuition that pure formula manipulation cannot.
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Physics Class 12 Part I – NCERT (2025-26)
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