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In the electric field shown in figure, the electric field lines on the left have half separation as that between those on the right. If the magnitude of the field at point A is \[60\text{ }N{{C}^{-1}},\] calculate the force experienced by a proton placed at point B. Also, find the magnitude of electric field at point B.         

Answer:

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  As given, the separation between electric field lines at point A is half of that at point B. Therefore,          \[{{E}_{A}}=2{{E}_{B}}\Rightarrow {{E}_{B}}=\frac{{{E}_{A}}}{2}\] \[\therefore \]                  \[{{E}_{B}}=\frac{60}{2}=30N/C\] We know, force on a charge in a electric field, F = qE. \[\therefore \]      \[{{F}_{B}}={{E}_{B}}q=1.6\times {{10}^{-19}}\times 30\]             \[=4.8\times {{10}^{-18}}N\]