2. Solved Papers
  3. WB JEE Medical

WB JEE Medical WB JEE Medical Solved Paper-2014

  • question_answer
    An infinite sheet carrying a uniform surface charge density \[\sigma \] lies on the \[xy-\]plane. The work done to carry  a charge q from the point \[A=a(\hat{i}+2\hat{j}+3\hat{k})\]to the point \[A=a(\hat{i}+2\hat{j}+3\hat{k})\](where a is a constant with the dimension of length and \[{{\varepsilon }_{0}}\]is the permittivity of free space) is

    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.
You will be redirected in 3 sec spinner