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Current or field for which the magnetic force balances a wire's weight

This type of question, asked 4 times: 28 Jul 2022, 30 Jan 2023, 13 Apr 2023, 5 Apr 2024. All 4 questions below, oldest first.

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  1. Question 1

    28 Jul 2022

    13
    As shown in the figure, a metallic rod of linear density 0.45 kg m−10.45\text{ }kg{\text{ }m}^{- 1} is lying horizontally on a smooth incline plane which makes an angle of 45∘45^{\circ} with the horizontal. The minimum current flowing in the rod required to keep it stationary, when 0.15 T0.15\text{ }T magnetic field is acting on it in the vertical upward direction, will be: {Use  g=10 m/s2}\left. \ g = 10\text{ }m/s^{2} \right\}

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  2. Question 2

    30 Jan 2023

    17
    A massless square loop, of wire of resistance 10Ω10\Omega, supporting a mass of 1 g1\text{ }g, hangs vertically with one of its sides in a uniform magnetic field of 103G10^{3}G, directed outwards in the shaded region. A dc voltage VV is applied to the loop. For what value of VV, the magnetic force will exactly balance the weight of the supporting mass of 1 g1\text{ }g ? (If sides of the loop =10 cm,g=10 ms−2= 10\text{ }cm,g = 10{\text{ }ms}^{- 2} )

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  3. Question 3

    13 Apr 2023

    120
    A straight wire ABAB of mass 40 g40\text{ }g and length 50 cm50\text{ }cm is suspended by a pair of flexible leads in uniform magnetic field of magnitude 0.40 T0.40\text{ }T as shown in the figure. The magnitude of the current required in the wire to remove the tension in the supporting leads is ____A. (Take  g=10 ms−2)\left. \ g = 10{\text{ }ms}^{- 2} \right).

  4. Question 4

    5 Apr 2024

    22
    A 2A current carrying straight metal wire of resistance 1Ω1\Omega, resistivity 2×10−6Ωm2 \times10^{- 6}\Omega m, area of cross-section 10 mm210{\text{ }mm}^{2} and mass 500 g500\text{ }g is suspended horizontally in mid air by applying a uniform magnetic field B→\overrightarrow{B}. The magnitude of BB is _____ ×10−1 T\times10^{- 1}\text{ }T (given, g=10 m/s2g = 10\text{ }m/s^{2} )