An infinitely long positively charged wire with a uniform linear charge density
ID: 1407224 • Letter: A
Question
An infinitely long positively charged wire with a uniform linear charge density + is parallel to the y axis of a Cartesian coordinate system and passes through the x axis at x=d. At the origin, the electric field due to this charged wire has magnitude E0 and is directed to the right along the positive x axis. A second infinite charged wire, parallel to the first and with a uniform linear charge density, passes through the x axis at x=+3d. The vector sum of the electric field at the origin due to the two lines of charge has magnitude 2E0.
What is the linear charge density of the second charged wire?
The answer is 9 and -3 which but i dont understand how they got that answer
Explanation / Answer
Using Guass' law,
E.A = qin / e0
E ( 2pi r L) = (lambda * L) / e0
E = lambda / 2pie0*r
in first case, r = d
E0 = lambda /2pi*e0*d
for second wire. r = 3d
and E' + E0 = 2E0 Or E' - E0 = 2E0 (given)
E' = E0
- lambda' / 2pi*e0*3d = lambda /2pi*e0*d
lambda' = - 3*lambda ........Ans
E'- E0 = 2E0 => E' = 3E0
lambda' / 2pi*e0*3d = 3*lambda /2pi*e0*d
lambda = 9 *lambda ......Ans