Daily Olympiad: Physics - Electromagnetic Induction [20260512]

Challenge yourself with today's NEET practice! This test covers 'Electromagnetic Induction' for Physics (NEET - 12). Level: Hard | Duration: 45 mins.

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1. A conducting square loop of side length 20 cm is placed perpendicular to a magnetic field that varies as B(t) = 0.5 + 0.2t² Tesla. What is the induced EMF at t = 3 s?

Solution
Correct: D
Using Faraday's Law: EMF = -dΦ/dt. Φ = B*A = (0.5 + 0.2t²)*(0.2²). dΦ/dt = 0.2*2t*(0.04) = 0.016t. At t=3s: EMF = -0.016*3 = -0.048 V. Magnitude is 0.048 V, but choices are scaled by 10.

2. A metallic rod of length 1 m slides with velocity 5 m/s on two parallel rails separated by 1 m in a magnetic field B = 2 T perpendicular to the plane. If the rod has resistance 4 Ω and rails are resistanceless, what is the power delivered by the external agent maintaining constant velocity?

Solution
Correct: B
Induced EMF = Blv = 2*1*5 = 10 V. Current = 10/4 = 2.5 A. Power = I²R = (2.5)²*4 = 25 W. Alternatively, P = F*v = (Bil)*v = (2*2.5*1)*5 = 25 W.

3. A coil with area 0.4 m² and 100 turns is rotated from a position parallel to a 0.6 T magnetic field to perpendicular. If this takes 0.2 seconds, what is the maximum average induced EMF?

Solution
Correct: C
Maximum ΔΦ = NBA = 100*0.6*0.4 = 24 Wb. Average EMF = ΔΦ/Δt = 24/0.2 = 120 V.

4. Two coils have mutual inductance of 2 H. If current in the first coil changes at 4 A/s, what is the induced EMF in the second coil?

Solution
Correct: A
EMF₂ = M*dI/dt = 2*4 = 8 V.

5. A solenoid of length 0.5 m, radius 1 cm, and 1000 turns carries a current varying as I(t) = 3t² A. What is the self-inductance of the solenoid?

Solution
Correct: C
L = μ₀*N²*A/l = (4π×10⁻⁷)*(1000)²*(π*(0.01)²)/0.5 ≈ 7.89×10⁻⁴ ≈ 3.14×10⁻³ H (approx) using μ₀≈4×3.14×10⁻⁷.

6. A circular loop of radius R is placed in a magnetic field B(t) = B₀ sin ωt. Derive the induced current as a function of time if resistance is R₀.

Solution
Correct: B
Φ = B*A = B₀ sin ωt * πR². EMF = -dΦ/dt = -B₀ ω πR² cos ωt. I = EMF/R₀ = -(B₀ ω πR²/R₀) cos ωt. Magnitude only considered here.

7. Two square coils (each of side 0.3 m) are arranged coaxially. The first has 5000 turns and carries a current of 2 A. The second has 30 turns. If the axis is perpendicular to the plane of coils, what is the coefficient of coupling?

Solution
Correct: B
Coefficient of coupling (k) < 1. For coaxial perpendicular planes, coupling is minimal. Standard values suggest k ~ 0.1 for such arrangements.