A 2A current carrying straight metal wire of resistance 1 Ω… | JEE Main 2024 (5 Apr, Shift 1)

Q21JEE Main 2024 · 5 APR · SHIFT 1Medium

Force on Current-Carrying Conductors

A 2A current carrying straight metal wire of resistance $1\ \Omega$ , resistivity $2 \times 10^{-6}\ \Omega\text{ m}$ , area of cross- section $10\text{ mm}^2$ and mass $500\text{ g}$ is suspended horizontally in mid air by applying a uniform magnetic field $\vec{B}$ . The magnitude of B is ________ $\times 10^{-1}\text{ T}$ (given, $g = 10\text{ m/s}^2$ ).

Numerical answer type. Work it out, then open the answer.

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Answer: 5

Length of the wire: $R = \frac{\rho L}{A} \Rightarrow L = \frac{RA}{\rho} = \frac{1\times10\times10^{-6}}{2\times10^{-6}} = 5\text{ m}$
Suspended in air: $ILB = mg$
$B = \frac{0.5\times10}{2\times5} = 0.5\text{ T} = 5\times10^{-1}\text{ T}$
So the answer is 5.

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