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Two point charges\[+8q\]and\[-2q\]are located at\[x=0\]and\[x=L\]respectively. The location of a point on the x-axis at which the net electric field due to these two point charges is zero, is     AIEEE  Solved  Paper-2005

A) 2L           

B)                        L/4           

C)        8L                           

D)        4L

Correct Answer: A

Solution :

Suppose that a point B, where net electric field is zero due to charges 8 q and The electric field at B due charge 8 q at O, and the electric field at B due to charge -2q at A, According to condition,            \[\frac{1}{4\pi {{\varepsilon }_{0}}}\,\frac{8q}{{{a}^{2}}}\,=\frac{1}{4\pi {{\varepsilon }_{0}}}\,\frac{2q}{{{(a+L)}^{2}}}\]                                     Thus, at distance 2L from origin, net electric field will be zero.