Question

A straight wire of mass $0.2kg$ and length $1.5m$ carries a current $2A$ is shown in the figure. It is suspended in midair by a uniform magnetic field $B$ pointing to the plane of paper. The magnitude of magnetic field is nearly?
(Ignore earth's magnetic field and assume $g=10m/s^2$).

• A. 0.55 T
• B. 0.67 T
• C. 0.75 T
• D. 0.85 T

Answer 1

Answer: (B)

Given, mass of the wire, $m=0.2kg$
Length of the wire, $l=1.5m$
Current, $I=2A$
The force acting on the current carrying wire in uniform magnetic field,
$F=IBl\sin \theta$
$F=IBl\sin 90^{\circ }\left(\because \theta =90^{\circ }\right)$
$F=IBl$...(i)
Weight of the wire, $w=mg=0.2\times 10N$
In the position of suspension,
$BIl=mg\Rightarrow B=\frac{mg}{Il}$
$=\frac{0.2\times 10}{2\times 1.5}=0.67T$