Question

A conductor $AB$ carries a current $i$ in a magnetic field $\overrightarrow{B}$. If $\overrightarrow{AB}=\overrightarrow{r}$ and the force on the conductor is $\overrightarrow{F}$.Then

• A. $\overrightarrow{F}$ does not depend on the shape of $AB$
• B. $\overrightarrow{F}=i(\overrightarrow{r}\times \overrightarrow{B})$
• C. $\overrightarrow{F}=i(\overrightarrow{B}\times \overrightarrow{r})$
• D. $|\overrightarrow{F}|=i(\overrightarrow{r}\cdot \overrightarrow{B})$

Answer 1

Answer: (A), (B)

The correct options are
A $\overrightarrow{F}$ does not depend on the shape of $AB$
B $\overrightarrow{F}=i(\overrightarrow{r}\times \overrightarrow{B})$

Motional emf between two point A and B $\epsilon ={\int }_A^B(\overrightarrow{v}\times \overrightarrow{B}).\overrightarrow{dl}=$ the component of $\overrightarrow{dl}$along $(\overrightarrow{v}\times \overrightarrow{B})$ is what matters.
$\therefore \epsilon$ does not depend upon the shape of $AB$.
Also force on a straight wire can be represented as $F=i(\overrightarrow{dl}\times \overrightarrow{B})=i(\overrightarrow{r}\times \overrightarrow{B})$