Question

A straight wire of mass $0.2\, kg$ and length $1.5\, m$ carries a current $2\, A$ 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 $g =10\, m / s ^{2}$).

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