A ceiling fan having 3 blades of length 80 ~cm each is rotating with an angular velocity of 1200 ~rpm. The magnetic…

Year	2026	2025	2024	Total
Questions	12	6	10	28

Year

2026

2025

2024

Total

Questions

Solution & Explanation

Related Formula

ε = (1)/(2) Bv ω ²

Bv = B δ

Core Logic

For a horizontal fan rotating in the Earth's magnetic field, the blades cut only the vertical component of the magnetic field ( $Bv$ $B_v$). The number of blades is a distractor, as they are all in parallel, meaning the EMF developed across one blade is the same as the EMF across the whole fan setup.

Step 1: Calculate Field and Omega

Vertical component of magnetic field:

Bv = B (30^°) = (0.5 \times 10⁻⁴ ~T) \times (1)/(2) = 0.25 \times 10⁻⁴ ~T = (1)/(4) \times 10⁻⁴ ~T

Angular velocity in rad/s:

ω = 2π f = 2π ((1200)/(60)) = 40π ~rad/s

Step 2: Calculate Induced EMF

Length of blade $= 80 ~cm = 0.8 ~m$ .

ε = (1)/(2) Bv ω ²

ε = (1)/(2) ((1)/(4) \times 10⁻⁴) (40π) (0.8)²

ε = (1)/(8) \times 10⁻⁴ \times 40π \times 0.64

ε = 5π \times 10⁻⁴ \times 0.64

ε = 3.2π \times 10⁻⁴ ~V

ε = 32π \times 10⁻⁵ ~V

Step 3: Extract N

Given $ε = Nπ \times 10⁻⁵ ~V$ , we can directly see that $N = 32$ $N = 32$.

Pattern Recognition

Motional EMF for rotating rods acts like a battery. Multiple identical blades radiating from the center to the rim behave like multiple identical batteries in parallel; the total voltage does not stack. Isolate $Bv$ $B_v$ for horizontal spinners.

Chapter Mix

Class 12 Physics: Electromagnetic Induction Class 12 Physics: Magnetism and Matter

More Electromagnetic Induction Previous-Year Questions — Page 6

Q53 jee_main_2024_31_jan_evening Faraday's Law

The magnetic flux

φ

(in weber) linked with a closed circuit of resistance

8 Ω

varies with time (in seconds) as

φ = 5t² - 36t + 1

. The induced current in the circuit at

t = 2 s

is ________ A.

Numerical Answer. Answer: 2 to 2

Solution

Related Formula

ε = -(dφ)/(dt)

I = (|ε|)/(R)

Core Logic

Calculate the time derivative of the magnetic flux to find the induced EMF. Evaluate it at the requested time, and then apply Ohm's law to find the current magnitude.

Step 1: Calculate Induced EMF

ε = -(d)/(dt) (5t² - 36t + 1)

ε = -(10t - 36)

At $t = 2 s$ $t = 2 \text{ s}$:

ε = - (10 \times 2 - 36)

ε = -(20 - 36) = 16 V

Step 2: Calculate Induced Current

I = (ε)/(R) = (16)/(8) = 2 A

Pattern Recognition

Flux polynomials ( $At² - Bt + C$ $At^2 - Bt + C$) instantly trigger a simple derivative test. Remember to drop the negative sign for final current magnitude unless direction is specifically asked.

Chapter Mix

Class 12 Physics: Electromagnetic Induction

Q jee_main_2024_31_jan_morning Mutual Inductance

A small square loop of wire of side

is placed inside a large square loop of wire of side

L

(

L = ²

). The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is

\sqrt(x) \times 10⁻⁷ H

, where

x =

Numerical Answer. Answer: 128 to 128

Solution

Related Formula

M = (φ₂)/(i₁)

Bstraight wire segment = (μ₀ i)/(4π d) ( θ₁ + θ₂)

Core Logic

Mutual Inductance diagram for Q57 - JEE Main 2024 Morning

Assume a current $i$ $i$ flows through the larger square loop of side $L$ $L$. The magnetic field generated by it at its center acts as a uniform field across the very small inner loop of side $\ell$.

The magnetic field at the center of the large square loop (distance $d = L/2$ $d = L/2$ from each side, angles $45^°$ $45^\circ$):

B = 4 \times [ (μ₀ i)/(4π (L/2)) ( 45^° + 45^°) ]

B = (μ₀ i)/(π (L/2)) ( 2\sqrt(2) )

B = 2\sqrt(2) μ₀ iπ L

Step 2: Mutual Inductance Calculation

Flux linkage for the inner loop:

φ = B \cdot ²

φ = 2\sqrt(2) μ₀ iπ L ²

Given $L = ²$ $L = \ell^2$:

φ = 2\sqrt(2) μ₀ iπ ( ²) ² = 2\sqrt(2) μ₀ iπ

Mutual inductance $M$ $M$:

M = (φ)/(i) = 2\sqrt(2) μ₀π

Using $μ₀ = 4π \times 10⁻⁷$ $\mu_0 = 4\pi \times 10^{-7}$:

M = 2\sqrt(2) \times 4π \times 10⁻⁷π

M = 8\sqrt(2) \times 10⁻⁷ H

M = \sqrt(128) \times 10⁻⁷ H

Comparing with $\sqrt(x) \times 10⁻⁷$ $\sqrt{x} \times 10^{-7}$, we get $x = 128$ $x = 128$.

Chapter Mix

Class 12 Physics: Electromagnetic Induction

Q44 jee_main_2024_31_jan_morning Faraday's Law

A coil is placed perpendicular to a magnetic field of

5000 ~T

. When the field is changed to

3000 ~T

2s

, an induced emf of

22 ~V

is produced in the coil. If the diameter of the coil is

0.02 ~m

, then the number of turns in the coil is:

A. $7$ $7$
B. $70$ $70$
C. $35$ $35$
D. $140$ $140$

Solution

Related Formula

ε = N | (Δφ)/(Δ t) |

Δφ = (Δ B) A θ

Core Logic

Given data: Initial Magnetic Field, $Bᵢ = 5000 T$ $B_i = 5000\mathrm{\,T}$ Final Magnetic Field, $Bf = 3000 T$ $B_f = 3000\mathrm{\,T}$ Time interval, $Δ t = 2 s$ $\Delta t = 2\mathrm{\,s}$ Diameter, $d = 0.02 m \Rightarrow r = 0.01 m$ Induced emf, $ε = 22 V$ $\varepsilon = 22\mathrm{\,V}$

Change in magnetic field magnitude $|Δ B| = 5000 - 3000 = 2000 T$ . Area of the coil $A = π r² = π (0.01)² = 10⁻⁴π m²$ .

Step 2: Equation Evaluation

Δφ = |Δ B| A = (2000) π (0.01)² = 0.2π

Using Faraday's Law:

22 = N ( (0.2π)/(2) )

$22 = N (0.1π)$ $22 = N (0.1\pi)$ Taking $π \approx 22/7$ $\pi \approx 22/7$:

22 = N ( 0.1 \times (22)/(7) )

1 = (N)/(70) \Rightarrow N = 70

Chapter Mix

Class 12 Physics: Electromagnetic Induction

Solution & Explanation

Related Formula

Core Logic

Step 1: Calculate Field and Omega

Step 2: Calculate Induced EMF

Step 3: Extract N

Pattern Recognition

Chapter Mix

Reference Study Guides

More Electromagnetic Induction Previous-Year Questions — Page 6

Solution

Related Formula

Core Logic

Step 1: Calculate Induced EMF

Step 2: Calculate Induced Current

Pattern Recognition

Chapter Mix

Solution

Related Formula

Core Logic

Step 2: Mutual Inductance Calculation

Chapter Mix

Solution

Related Formula

Core Logic

Step 2: Equation Evaluation

Chapter Mix

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Solution & Explanation

Related Formula

Core Logic

Step 1: Calculate Field and Omega

Step 2: Calculate Induced EMF

Step 3: Extract N

Pattern Recognition

Chapter Mix

Reference Study Guides

More Electromagnetic Induction Previous-Year Questions — Page 6

Solution

Related Formula

Core Logic

Step 1: Calculate Induced EMF

Step 2: Calculate Induced Current

Pattern Recognition

Chapter Mix

Solution

Related Formula

Core Logic

Step 2: Mutual Inductance Calculation

Chapter Mix

Solution

Related Formula

Core Logic

Step 2: Equation Evaluation

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