Electrostatic field ( Gauss Law )

[Saru]

Homework Statement

Assuming that an infinitely long line charge of 50(pC/m) parallel to the y-axis at x=2(m) and z=1(m), determine the electric intensity at the point (-1, 5, -3).

The answer given : -0.18(a_x0.6 + a_z0.8)(V/m)

Homework Equations

Electric field intensity due to an infinite straight line charge of uniform density :
E= a_r("rho" / (2"pi""epsolon 0"r) ( V/m)

The Attempt at a Solution

I let point P = -a_x + a_y5 - a_z3
Point on line perpendicular to point P, Q = a_x2 + a_z

Vector Q to P = -a_x3 + a_y5 - a_z4

I found out that if i ignore or make coefficient of a_y to zero and apply the above formula i'll get the answer..

but i do not understand why..please help

 

[dx]

Hi Saru,

Draw a picture and you will see the reason immediately. You are not looking for the distance from P to Q, but from P to the line of charge.

 

[Mene]

The reason why you can ignore the coefficient of ay in this problem is because the line charge is parallel to the y-axis. This means that the electric field at point P will only have a component in the x and z directions, since the line charge is not affecting the electric field in the y direction. Therefore, the coefficient of ay in the answer is zero.