A) \[{{B}_{0}}\,\,i\,\,\ell \]
B) \[\sqrt{2}\,\,{{B}_{0}}\,\,i\,\,\ell \]
C) \[2\,\,{{B}_{0}}\,\,i\,\,\ell \]
D) \[{{B}_{0}}\,\,i\,\,\ell \,\,/\sqrt{2}\]
Correct Answer: B
Solution :
| Magnetic force on wire \[=i\,(\vec{\ell }\times \vec{B})\] |
| Where \[\vec{\ell }=\ell \hat{i}\](as wire is lying along x- axis) |
| \[\vec{B}=B.(\hat{i}+\hat{j}+\hat{k})\] |
| \[\therefore \,\,\,\,\vec{F}=I\vec{\ell }\times \vec{B}\] |
| \[\Rightarrow I\ell \,\,(\hat{i})\times {{B}_{0}}\,\,(\hat{i}+\hat{j}+\hat{k})\] |
| \[\vec{F}={{B}_{0}}I\ell (\hat{k}-\hat{j})\] |
| \[\Rightarrow \vec{F}=\sqrt{2}\,{{B}_{0}}I\ell \] |
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