# Force of interaction between two halves of a cylinder of charge.

• Lavabug
In summary, the task is to find the force of interaction per unit length between the upper and bottom halves of a cylinder with uniform charge density rho. The solution provided is \rho^2R^3/3\epsilon_0. However, the conversation discusses the difficulty of finding an analytic expression for the field of half a cylinder and suggests finding the interaction energy first and then taking its gradient. It is mentioned that the problem assumes a separation of 0 between the two halves and therefore, the field is just the field inside an infinitely long cylinder. Further discussion involves dividing the expression for charge inside \rho.r^2/R^2 by the surface of a finite cylinder 2pi*rL, but this does not lead to the correct
Lavabug

## Homework Statement

Find the force of interaction per unit length between the upper and bottom halves of a cylinder of uniform charge density rho.

## Homework Equations

Solution should be $\rho^2R^3/3\epsilon_0$

## The Attempt at a Solution

Frustrated cause I've solved this problem in the past and don't recall how to do it.

There's no analytic expression for the field of half a cylinder yes? How would I start to set the problem up? Would I have to find the interaction energy first then take its gradient?

There's no analytic expression for the field of half a cylinder yes? How would I start to set the problem up? Would I have to find the interaction energy first then take its gradient?

I think the problem is assuming that the separation between the two halves is 0. If not, it would have given you the separation, which it didn't. So the field is just the field inside an infinitely long cylinder.

ideasrule said:
I think the problem is assuming that the separation between the two halves is 0. If not, it would have given you the separation, which it didn't. So the field is just the field inside an infinitely long cylinder.

For the E field I just divided my expression for charge inside$\rho.r^2/R^2$ by the surface of a finite cylinder 2pi*rL. Doesn't get me anywhere near the answer.

## 1. What is the force of interaction between two halves of a cylinder of charge?

The force of interaction between two halves of a cylinder of charge is known as Coulomb's law and is given by the equation F = k(q1q2)/r^2, where k is the Coulomb's constant, q1 and q2 are the charges of the two halves, and r is the distance between them.

## 2. How does the force of interaction between two halves of a cylinder of charge change with distance?

The force of interaction between two halves of a cylinder of charge is inversely proportional to the square of the distance between them. This means that as the distance between the two halves increases, the force decreases and vice versa.

## 3. Can the force of interaction between two halves of a cylinder of charge be attractive?

Yes, the force of interaction between two halves of a cylinder of charge can be attractive or repulsive depending on the charges of the two halves. If the charges are of opposite signs, the force will be attractive, and if they are of the same sign, the force will be repulsive.

## 4. How does the size of the charges affect the force of interaction between two halves of a cylinder of charge?

The larger the charges of the two halves of the cylinder, the stronger the force of interaction will be. This is because the force is directly proportional to the magnitude of the charges.

## 5. Can the force of interaction between two halves of a cylinder of charge be zero?

Yes, if the charges of the two halves are equal in magnitude and opposite in sign, the force of interaction between them will be zero. This is because the forces will cancel each other out, resulting in a net force of zero.

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