Electric field due to charged rods

[-EquinoX-]

Homework Statement

If I have a charged vertical rod and a point P which is distanced x from the perpendicular bisector of it. How do I find the electric field at P if x/(/l/2) < 1, where l is the length of the rod

Homework Equations

The Attempt at a Solution

I know that the equation of an electric field due to a charged rod at P is:

$$\frac{\lambda L}{(4 \pi \epsilon_0) * sqrt(x^2 + L^2/4)}$$

I don't know how to proceed further

 

[LowlyPion]

I'd draw a diagram and write a formula for a uniform line of charge and evaluate the integral over the range of the coordinates for the length of the rod.

 

[nlightner]

with this equation since it involves a perpendicular bisector. Could you please provide some guidance?
To find the electric field at point P, we can use the equation you mentioned, which calculates the electric field due to a charged rod at a point x distance away from it. However, in this case, we need to take into account the distance from the perpendicular bisector of the rod, which is L/2. This distance will affect the electric field at point P.

To incorporate this distance, we can use the Pythagorean theorem to find the distance between point P and the perpendicular bisector of the rod, which is sqrt(x^2 + L^2/4). This distance will be the new value for x in the electric field equation.

Therefore, the new equation for the electric field at point P will be:

\frac{\lambda L}{(4 \pi \epsilon_0) * sqrt(x^2 + L^2/4)}

I hope this helps. Let me know if you have any further questions.