- #1

Rahulrj

- 107

- 0

## Homework Statement

Find the electric field of an infinitely long straight wire of charge ## \lambda## C/m at a point ##r= ix+jy##

## Homework Equations

##\int E.da = \frac {Q}{\epsilon_0}##

##E= \frac{\int dq}{4\pi\epsilon_0 r^2} ##

*r*

## The Attempt at a Solution

Drawing a cylindrical gaussian surface of radius 's' I can find E, using the gauss's law:

##E.2 \pi s L = \frac {\lambda L}{\epsilon_0}##

##E = \frac{\lambda}{2\pi s\epsilon_0}##

So is my answer correct if I just substitute the given 'r' into the above equation for 's'? which is ##E = \frac{\lambda}{ 2\pi (ix+iy) \epsilon_0} ##

*r*(where r is unit vector) I find it bit odd.

Alternatively when I try to find E using the electric field formula from Coloumb's law, I am stuck with the integration as the wire extends from negative to positive infinity and I am not sure of how to include vector into it.

##E= \frac{\int dq}{4\pi\epsilon_0 r^2}##

##dq = \lambda dl##

If i assume wire to be lying on the x - axis, how should I write the separation vector r in the above equation?

Is it ##r_* = xi+yj-xi = yj## thereby ##r=y^2## or just directly substituting ##r =xi +yj## I am just confused with the vectors here.

Last edited: