A straight wire of mass 100 g and length 1.5 m carries a current of 2 A. It is suspended in mid air by a uniform horizontal magnetic filed as shown in the figure. What is the magnitude of the magnetic field? (acceleration due to gravity = $10 ms^{-2}$.)

0.33 T

The correct answer is Option (1) → 0.33 T

Mass of wire, $m=0.1kg$

$g=10m/s^2$ [Acceleration due to gravity]

$F_{gravity}=0.1×10=1N$

$F_{magnetic}=ILB\sin θ$

where,

$I=2A$

$L=1.5m$

B = magnetic field strength

$θ=90°$

$∴ F_{magnetic}=F_{gravity}$

$ILB=mg$

$2×1.5×B=1$

$B=\frac{1}{2×1.5}=\frac{1}{3}T$