A massless square loop, of wire of resistance $10\,\Omega$. supporting a mass of $1\,g$. hangs vertically with one of its sides in a uniform magnetic field of $10^3\, G$, directed outwards in the shaded region. A dc voltage $V$ is applied to the loop. For what value of V. the magnetic force will exactly balance the weight of the supporting mass of $1\,g$ ? (If sides of the loop $=10\,cm , g =10\,ms ^{-2}$ )
JEE MAIN 2023, Medium
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$F _{ m }= mg$
$\therefore \quad ILB = mg$
$\therefore \quad\left(\frac{ V }{ R }\right) LB = mg$
$\therefore \quad V =\frac{ mgR }{ LB }$
$=\frac{\left(1 \times 10^{-3}\,kg \right)\left(10\,m / s ^2\right)(10 \Omega)}{(0.1\,m )\left(10^3 \times 10^{-4}\,T \right)}=10\,V$
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