Electric Field Between/Above Parallel Charged Rods

[Fusilli_Jerry89]

Homework Statement

2 uniformly charged very long (L -> infinite) straight, parallel rods d cm apart each carry a linear charge density +lambda and -lambda.
Find the magnitude and direction of the electric field between the 2 rods (x=0, -d/2 < z < d/2) and above the rods (x=0, z > d/2)


________________________________

---------------------------------------------->x
________________________________ (z is vertical axis)

Homework Equations

E = q/4(pi)(epsilon)(r^2)

The Attempt at a Solution

First of all, would E be zero above the 2 rods? The question also has a b part to it that asks what the behavior is if z is much greater than d. I guessed that E was not zero above the 2 rods since it seemed like there were so many marks for finding E above the rods, but was I wrong? If not, do you calculate E above the rods the pretty much the same way as below only subtract them instead of add them?

For E between the rods:
dE = q/4(pi)(epsilon)(x^2 + (d^2)/4)
cos(theta) = (d/2)/(x^2 + (d^2)/4)^.5
dEz = qd/8(pi)(epsilon)(x^2 + (d^2)/4)^3/2

Ez = [qd/8(pi)(epsilon)] * integral from -L/2 to L/2 of (x^2 + (d^2)/4)^-3/2 dx
Ez = qL/2(pi)(epsilon)d
since there are two rods, we multiply this by 2:
E = qL/(pi)(epsilon)d

is this method/approach correct? Thx

 

[Shooting Star]

The Attempt at a Solution

First of all, would E be zero above the 2 rods? The question also has a b part to it that asks what the behavior is if z is much greater than d. I guessed that E was not zero above the 2 rods since it seemed like there were so many marks for finding E above the rods, but was I wrong? If not, do you calculate E above the rods the pretty much the same way as below only subtract them instead of add them?

E would not be zero above the rods -- that happens with infinite planes.

You have to know the field of an infinite wire at a dist r. This is done in all the books, so I'll just give it here:

$$\frac{1}{4\pi\epsilon_{0}} \frac{2\lambda}{r}.$$

The direction of the field is obvious.

You have to take the vector sum of the fields due to the two rods. In this case, since both the fields are in the same line, just adding or subtracting will do. To find it at a large distance, take the limit of z tending to infinity.

If you look at the two rods from a great distance, how do you feel it should look like?

 

[Moetasim]

I would say that your approach and method seem to be on the right track. However, I would recommend double-checking your calculations and equations to ensure accuracy. Additionally, I would suggest considering the concept of superposition, which states that the total electric field at a point is the vector sum of the individual electric fields from each charge. This may help you in calculating the electric field above the rods. Also, to answer your question, the electric field above the rods would not be zero, as there are charges present on the rods that would create an electric field. Overall, your understanding of the topic and your approach to solving the problem seem to be correct, but I would suggest reviewing and double-checking your calculations for accuracy.