A) \[\hat{k}\]
B) \[-\left( \frac{\hat{i}+\hat{j}}{\sqrt{2}} \right)\]
C) \[-\hat{k}\]
D) \[\frac{\hat{i}+\hat{j}}{\sqrt{2}}\]
Correct Answer: D
Solution :
[d] \[\overset{\to }{\mathop{B}}\,=-c\hat{k}\], and \[\overset{\to }{\mathop{v}}\,=v\,\cos \,{{45}^{o}}\hat{i}-v\,\sin \,{{45}^{o}}\hat{j}\] \[=\frac{v}{\sqrt{2}}\hat{i}-\frac{v}{\sqrt{2}}\hat{j}\]. Thus, \[\overset{\to }{\mathop{F}}\,=q(\overset{\to }{\mathop{v}}\,\times \overset{\to }{\mathop{B}}\,)=q\left[ \left( \frac{v}{\sqrt{2}}\hat{i}-\frac{v}{\sqrt{2}}\hat{j} \right)\times (-c\hat{k}) \right]\] \[=qcv\left[ \frac{\hat{i}+\hat{j}}{\sqrt{2}} \right]\] \[\therefore \,\,\,\overset{\to }{\mathop{a}}\,=\left[ \frac{\hat{i}+\hat{j}}{\sqrt{2}} \right]\]
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