Question

A current carrying conductor of mass $m$ is floating in air such that it is making an angle $\theta$ with the direction of magnetic field. The conductor and uniform magnetic field both lie in horizontal plane. Then the value of current $i$ in the conductor will be:$($length of conductor is $l$, magnetic field induction is $B)$

• A. $\frac{2mg}{Bl\sin \theta }$
• B. $\frac{mg}{Bl\sin \theta }$
• C. $\frac{mg}{2Bl\sin \theta }$
• D. $\frac{mg}{4Bl\sin \theta }$

Answer 1

The correct option is B $\frac{mg}{Bl\sin \theta }$

The scenario described in the question can be represented with the following diagram:


From using relation, $\overrightarrow{F}=i(\overrightarrow{l}\times \overrightarrow{B})$,
the direction of magnetic force is coming normally outwards to the plane of conductor. So,

$F=Bil\sin (\pi -\theta )=Bil\sin \theta$



Applying equilibrium condition on conductor;
$F=mg$

$\Rightarrow Bil\sin \theta =mg$

$\therefore i=\frac{mg}{Bl\sin \theta }$

Hence, option (b) is the correct answer.