A) \[\frac{2{{\eta }^{2}}}{g{{a}^{2}}}\]
B) zero
C) \[\frac{{{\eta }^{2}}}{g{{a}^{2}}}\]
D) \[\frac{{{\eta }^{2}}}{2g{{a}^{2}}}\]
Correct Answer: D
Solution :
Consider an elementary portion of the ring. Electric field at the centre due this elementary portion is \[{{v}_{P}}=v,\,\,{{v}_{Q}}=0\] \[{{v}_{P}}={{v}_{Q}}=0\] If we consider upper portion of the ring x-components of electric field cancelled out. Net electric field will be due to addition of the y-components. \[{{v}_{P}}=0,{{v}_{Q}}=2v\] \[\eta \] \[\lambda \] \[\frac{2\eta }{\lambda }[1-{{e}^{-\lambda t}}]\] Similarly due to lower portion net electric field \[\frac{\eta }{2\lambda }[1-{{e}^{-\lambda t}}]\] \[\frac{\eta }{{{\lambda }^{2}}}[1-{{e}^{-{{\lambda }^{2}}t}}]\] Total electric field \[\frac{\eta }{\lambda }[1-{{e}^{-\lambda t}}]\]You need to login to perform this action.
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