Question

Calculate the total electric flux leaving the cylinder surface r=4.5, z=±3.5, given the charge configuration; i) 2 C point charge on the x-axis at x=0, ±1, ±2, …..; ii) a line charge on the x-axis ρ_L=2 cos 0.1x C/m.​

Answer 1

Let x=0.47ˉ  (Mixed recurring decimal)

i.e. x=0.47777…(1)

Multiplying (1) by 10, to make it pure recurring decimal, we get

10x=4.7777…(2)

Further multiplying (2) by 10, we get

100x=47.777….(3)

Subtracting (2) from (3), we get

100x–10x=(47.777…)–(4.7777…)

⇒90x=43

⇒x=9043

Thus 0.47ˉ=9043