Question

A conductor ab of arbitrary shape carries current $I$ flowing from b to a.The length vector $\overrightarrow{ab}$ is oriented from a to b.The force $\overrightarrow{F}$ experienced by this conductor in a uniform magnetic field $\overrightarrow{B}$ is

• A. $\overrightarrow{F}=-I(\overrightarrow{ab}\times \overrightarrow{B})$
• B. $\overrightarrow{F}=I(\overrightarrow{B}\times \overrightarrow{ab})$
• C. $\overrightarrow{F}=-I(\overrightarrow{ba}\times \overrightarrow{B})$
• D. all of these

Answer 1

Answer: (A), (B)

The correct options are
A $\overrightarrow{F}=-I(\overrightarrow{ab}\times \overrightarrow{B})$
B $\overrightarrow{F}=I(\overrightarrow{B}\times \overrightarrow{ab})$

Force experienced $\overrightarrow{F}=I(\overrightarrow{l}\times \overrightarrow{B})$ where $\overrightarrow{l}$ points in the direction of current flow i.e $\overrightarrow{ba}$

$\therefore$ $\overrightarrow{F}=I(\overrightarrow{ba}\times \overrightarrow{B})$

Using $\overrightarrow{ba}=-\overrightarrow{ab}$ $⟹$ $\overrightarrow{F}=-I(\overrightarrow{ab}\times \overrightarrow{B})$

Also $\overrightarrow{X}\times \overrightarrow{Y}=-(\overrightarrow{Y}\times \overrightarrow{X})$

$⟹$ $\overrightarrow{F}=I(\overrightarrow{B}\times \overrightarrow{ab})$ .