Question

A conductor of length $l$ and mass $m$ carrying $i$ is placed on a smooth incline plane making an angle $\theta$ with horizontal. A magnetic field $B$ is directed vertically upwards. Then for equilibrium of the conductor $\cot \theta$ is given by

• A. $\frac{BiL}{mg}$
• B. $\frac{mg}{BiL}$
• C. $\frac{mg}{BiL}$
• D. $\frac{mg}{2BiL}$

Answer 1

The correct option is B $\frac{mg}{BiL}$

The magnetic force exerted on the current carrying wire $F$ is in horizontal direction is given by,

$F=BiL$


From $FBD$ under the equilibrium,

$mg\sin \theta =BiL\cos \theta$

$\therefore \cot \theta =\frac{mg}{BiL}$ ​

Hence, option(b) is the correct answer.