Question

1. Two point charge of - 27x10^-6C and +64x10^-6C are 25cm in air, where can a third charge be located so that no net electrostatic force acts on it.

2.An infinite number of charges equal 10pC are placed along the X-axis at X = 20cm, X =40m, X =80m and so on. Find the electric intensity at the origin due to the given set of charge.

Answer 1

1)

$$\frac{27}{d^2}=\frac{64}{(25+d)^2}\\d=46.3\ cm$$

2)

$$E=9\cdot10^{9}\frac{10\cdot10^{-12}}{0.2}\sum \frac{1}{2^n}\\E=9\cdot10^{9}\frac{10\cdot10^{-12}}{0.2}\frac{4}{3}=0.6\frac{V}{m}$$