Question

Two infinitely long line charges each of linear charge density lambda are p two infinitely long line charges each of linear charge density lambda are placed at an angle theta.Find out electric field intensity at a point p , which is at a distance x from point o along angle bisector of line charges

Answer 1

two infinitely long line charges each of linear charge density lambda are placed at an angle theta.Find out electric field intensity at a point p , which is at a distance x from point o along angle bisector of line charges

solution : it is given that, OP = x

so, r = xsin(θ/2) .......(1)

electric field due to each wire at P , E = $\frac{\lambda}{2\pi\epsilon_0r}$..........(2)

now, resultant electric field at P = $\sqrt{E^2+E^2+2E^2cos\theta}$

=$E\sqrt{2+2cos\theta}$

= $E\sqrt{2\left(2cos^2\frac{\theta}{2}\right)}$

= $2Ecos\frac{\theta}{2}$

from equations (2),

= $\frac{\lambda}{\pi\epsilon_0r}cos\frac{\theta}{2}$

= $\frac{\lambda}{\pi\epsilon_0xsin\frac{\theta}{2}}cos\frac{\theta}{2}$

= $\frac{\lambda}{\pi\epsilon_0x}cot\frac{\theta}{2}$

[ note : plz converts this answer in required form. as I dunno what is answer mentioned in your book ]

Answer 2

Answer: I think the attachment will help you .