question_answer

Two small charged spheres A and B have charges 10 \[\mu C\] and 40 \[\mu C\] respectively, and            are held at a separation of 90 cm from each   other. At what distance from A, electric                intensity would be zero?

A) 22.5cm                                 

B) 18 cm

C) 36 cm                                   

D) 30 cm

Correct Answer: D

Solution :

Let at point D intensity is zero \[\therefore \] \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{10\times {{10}^{-6}}}{{{x}^{2}}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{40\times {{10}^{-6}}}{{{(90-x)}^{2}}}\]                 \[\frac{1}{{{x}^{2}}}=\frac{4}{{{(90-x)}^{2}}}\] \[\Rightarrow \]               \[\frac{1}{x}=\frac{2}{90-x}\] \[90-x=2x\] \[\Rightarrow \]               \[3x=90\] \[\therefore \] \[x=30\text{ }cm\]