A) \[\frac{3\sigma aq}{2{{\varepsilon }_{0}}}\]
B) \[\frac{2\sigma aq}{{{\varepsilon }_{0}}}\]
C) \[\frac{5\sigma aq}{2{{\varepsilon }_{0}}}\]
D) \[\frac{3\sigma aq}{{{\varepsilon }_{0}}}\]
Correct Answer: A
Solution :
The given \[A=a(\hat{i}+2\hat{j}+3\hat{k})\] \[B=a(i-2\hat{j}\,+6\hat{k})\] \[AB=OB-OA\] \[=a(\hat{i}-2\hat{j}+6\hat{k})-a(\hat{i}+2\hat{j}+3\hat{k})\] \[AB=a(-4\hat{j}\,+3\hat{k})\] Work done \[=q\left( \frac{\sigma }{2{{\varepsilon }_{0}}} \right)\hat{k}.AB\](along to Z-axis) \[=q\left( \frac{\sigma }{2{{\varepsilon }_{0}}} \right)\hat{k}.a(-4\hat{j}+3\hat{k})=\frac{3q\sigma a}{2{{\varepsilon }_{0}}}\] \[(\because \,\,\hat{i}.\hat{i}=\hat{j}.\hat{j}=\hat{k}.\hat{k}=1\,\text{and}\,\text{\hat{i}}\text{.\hat{j}}\,\,\text{=}\,\text{\hat{j}}\text{.\hat{k}}\,\text{=}\,\text{\hat{k}}\text{.\hat{i}}\,\text{=}\,\text{0})\]You need to login to perform this action.
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