Question

Two straight segments of wire $ab$ and $bc$ each carrying current $I$, are parallel as shown in fig. The cube edge is 50 cm and magnetic field is uniform along Y-axis having magnitude $0.4T$. If $I=3A$, the force experienced by wire abc in the presence of magnitude field is :

• A. $0.6\hat{i}$
• B. $1.2(\hat{i}+\hat{k})$
• C. $0.6(\sqrt{2}\hat{i}+\hat{j}-\sqrt{2}\hat{k})$
• D. $0.6(\sqrt{2}\hat{i}-\hat{k})$

Answer 1

The correct option is A $0.6\hat{i}$

Wire abc can be replaced by a straight wire ac for the computation of force.
$\overrightarrow{r_A}=a\hat{i}+a\hat{k}$
$\overrightarrow{r_C}=a\hat{i}+a\hat{j}$
$\overrightarrow{l}=\overrightarrow{ac}=\overrightarrow{r_C}-\overrightarrow{r_A}=a\hat{j}-a\hat{k}$
$\overrightarrow{F_m}=i(\overrightarrow{l}\times \overrightarrow{B})=i\left(\right(a\hat{j}-a\hat{k})\times \overrightarrow{B})=3\times 50\times {10}^{-2}(\hat{j}-\hat{k})\times \left(0.4\hat{j}\right)=0.6\hat{i}$