A) \[\vec{E}=-{{\upsilon }_{0}}{{B}_{0}}\left( \hat{i}+\hat{j}+7\hat{k} \right)\]
B) \[\vec{E}=-{{\upsilon }_{0}}{{B}_{0}}\left( 3\hat{i}-2\hat{j}-4\hat{k} \right)\]
C) \[\vec{E}={{\upsilon }_{0}}{{B}_{0}}\left( 14\hat{i}+7\hat{k} \right)\]
D) \[\vec{E}={{\upsilon }_{0}}{{B}_{0}}\left( 14\hat{j}+7\hat{k} \right)\]
Correct Answer: D
Solution :
| [d] \[{{F}_{e}}={{F}_{n}}=0\] |
| \[{{F}_{e}}=-{{F}_{m}}\] |
| \[=-q\left( \vec{v}\times \vec{B} \right)\] |
| \[=-{{\upsilon }_{0}}{{v}_{0}}\left[ \left( 3\hat{i}-\hat{j}+2\hat{k} \right)\times \left( \hat{i}+2\hat{j}-4\hat{k} \right) \right]\] |
| \[=-{{\upsilon }_{0}}{{v}_{0}}\left( 14\hat{i}+7\hat{k} \right)\] |
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