Finding the force from two charged rods one beside the other.

[Eats Dirt]

Homework Statement

The problem is to find the electric force between two rods one beside the other. a charge of Q is distributed over the rods uniformly each of length 2x. The centre of each rod is d from the others centre.




-----Rod 1------- ------Rod 2-------

Homework Equations

$$F= \frac{qq}{Kr^2}$$

$$Efield= \frac{q}{Kr^2}$$

The Attempt at a Solution

I know I am supposed to find the electric field over the whole distance then integrate the the length of one rod (I think) but I don't understand at all why this work

I would set the electric field up by

dq = Q/2x (Charge density) * dx

E= dq/(Kr^2) I think. then I am not even sure if I did that right and I think I'm supposed to integrate this over the length of 1 of the rods but I don't understand how that gives you force. Any help would be appreciated thanks!

 

[voko]

You need to find the electric field of a rod at an arbitrary location along its axis (outside itself). Then you need to consider how that field acts on another rod. You can do that by considering how it acts on each particle of the other rod - what is the net force then?

 

[Eats Dirt]

You need to find the electric field of a rod at an arbitrary location along its axis (outside itself). Then you need to consider how that field acts on another rod. You can do that by considering how it acts on each particle of the other rod - what is the net force then?

ok at an arbitrary distance outside of the first rod would would be "d" then integrate with respect for dx for the length of the first rod. What I don't get is how to do the second integral, what do we integrate with respect to? The distance "d" to the second rod? or do we just keep d and do the integral with respect to the length of the second rod?

 

[voko]

At any given point of the second rod, the electric fields of the first rod (found with the first integral) exerts a force on the second rod.

 

[Nickie]

I would approach this problem by first setting up the relevant equations and understanding the physical principles involved. The electric force between two charged rods can be calculated using Coulomb's law, which states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. In this case, we have two rods with charges Q distributed uniformly over their lengths, so we can use the equation F= (Q1*Q2)/ (4πε0d^2), where d is the distance between the centers of the rods.

To find the force between the two rods, we need to first calculate the electric field at a point on one rod due to the other rod. This can be done by using the equation E= (Q/(4πε0r^2)), where Q is the charge on the other rod and r is the distance from the point to the center of the other rod. We can then integrate this electric field over the length of one rod, taking into account the charge distribution along the rod. This will give us the total electric field at a point on one rod due to the other rod.

Once we have the electric field, we can use the equation F= qE, where q is the charge at that point on the rod, to calculate the force at that point. We can then integrate this force over the length of the rod to get the total force between the two rods.

In summary, to find the force between two charged rods, we need to first calculate the electric field at a point on one rod due to the other rod, then integrate this electric field over the length of one rod, and finally integrate the resulting force over the length of the rod to get the total force between the two rods. This approach is based on the principles of Coulomb's law and the relationship between electric field and force.