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Peak emf in a loop placed in a sinusoidally varying field

This type of question, asked 3 times: 10 Apr 2023, 23 Jan 2026 S2, 6 Apr 2026 S2. All 3 questions below, oldest first.

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  1. Question 1

    10 Apr 2023

    111
    A square loop of side 2.0 cm2.0\text{ }cm is placed inside a long solenoid that has 50 turns per centimetre and carries a sinusoidally varying current of amplitude 2.5 A2.5\text{ }A and angular frequency 700rads−1700rads^{- 1}. The central axes of the loop and solenoid coincide. The amplitude of the emf induced in the loop is x×10−4 Vx \times10^{- 4}\text{ }V. The value of xx is___ (Take, π=227\pi =\frac{22}{7} )

  2. Question 2

    23 Jan 2026 S2

    17
    Suppose a long solenoid of 100 cm length, radius 2 cm having 500 turns per unit length, carries a current I=10sin⁡(ωt)AI = 10\sin(\omega t)A, where ω=1000rad./s\omega = 1000rad./s. A circular conducting loop (B) of radius 1 cm coaxially slided through the solenoid at a speed =1 cm/s= 1\text{ }cm/s. The r.m.s. current through the loop when the coil B is inserted 10 cm inside the solenoid is α/2μ A\alpha/\sqrt{2}\mu\text{ }A. The value of α\alpha is ____\_\_\_\_ . [Resistance of the loop =10Ω= 10\Omega ]

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  3. Question 3

    6 Apr 2026 S2

    14
    A square loop of side 2 cm is placed in a time varying magnetic field with magnitude as B=0.4sin⁡(300t)B = 0.4\sin(300t) Tesla. The normal to the plane of loop makes an angle of 60∘60^{\circ} with the field. The maximum induced emf produced in the loop is ____\_\_\_\_ mV .

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