Q 12-04-074JEE MainJEE Main 2024 (5 Apr, Shift 1)Medium
A straight metal wire carrying a current of $2\ \text{A}$, having resistance $1\ \Omega$, resistivity $2\times10^{-6}\ \Omega\,\text{m}$, 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 ______ $\times10^{-1}\ \text{T}$ (given $g = 10\ \text{m/s}^2$).
Numerical value type. Enter your answer.
Answer: 5
Length of the wire: $L = \dfrac{RA}{\rho} = \dfrac{1\times10\times10^{-6}}{2\times10^{-6}} = 5\ \text{m}$.
Magnetic force balances weight:
$$BIL = mg \Rightarrow B = \frac{0.5\times10}{2\times5} = 0.5\ \text{T} = 5\times10^{-1}\ \text{T}$$
Solution by Sreeraj P, M.Sc Physics