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