question_answer

Two point charges \[+4q\] and \[+g\] are placed 30 cm apart. At what point on the line joining them is the electric field zero?

A)  \[15\,cm\] from charge \[4q\]

B)  \[20\,cm\] from charge \[4q\]

C)  \[7.5\,cm\] from charge q

D)  \[5\,cm\] from charge q

Correct Answer: B

Solution :

Suppose the point is a the distances x and \[{{x}_{2}}\] from the two charges, then \[\frac{K\,(4q)}{r_{1}^{2}}=\frac{K(q)}{r_{2}^{2}}\]             \[\Rightarrow \]   \[\frac{{{r}_{1}}}{{{r}_{2}}}=2\] and \[{{r}_{1}}+{{r}_{2}}=30\] Hence,       \[{{r}_{1}}=20\,cm\]