# Question from Electrostatics -- Charged beads on a wire...

1. Jul 5, 2016

### Ankit Chowdhury

1. The problem statement, all variables and given/known data

On a long friction-less non-conducting straight needle are threaded an infinitely large number of identical beads.The beads are made of insulating materials and have charges of equal magnitude and alternate plus and minus signs.Assume charge distribution on a bead unaffected by other charges in its vicinity. If the first bead is pulled out with a gradually increasing force, where will the chain break first?

2. The attempt at a solution I have thought of making a variable function of Tension on the string and then differentiate it for the max value to get the position.but I have no idea about how I am going to make the equation.

2. Jul 5, 2016

### Staff: Mentor

What is the equation for the force between each pair of beads?

3. Jul 5, 2016

### rude man

Not sure why there should be a "break" at all ...

4. Jul 5, 2016

### Ankit Chowdhury

I have already written the whole question and only this much of information was given .

5. Jul 5, 2016

### Staff: Mentor

But from your textbooks and lectures, you know an equation for the force between two charged objects as a function of distance. What is that equation and how can you use it in this problem?

6. Jul 5, 2016

### Ankit Chowdhury

Wait let me upload the picture of the question.

7. Jul 5, 2016

8. Jul 5, 2016

### Ankit Chowdhury

See question no. 26

9. Jul 5, 2016

### Staff: Mentor

You still have not answered my question about the equation... Please show some effort on this schoolwork problem of yours.

10. Jul 5, 2016

### Ankit Chowdhury

That equation is called column's law where force is directly proportional to the multiplication of two charges and inversely proportional to the square of the distance between the two charges.But I am unable to figure out that how will I apply this here.

11. Jul 5, 2016

### Staff: Mentor

Good! So can you write an equation for the force on the first bead from all of the other beads? It will be an infinite series. And then write the equation for the forces on the 2nd bead and so on. Then think about the forces on each bead as the first one is pulled a tiny bit away from the rest...

12. Jul 5, 2016

### Ankit Chowdhury

OK thanks I will try it .

13. Jul 5, 2016

### Ankit Chowdhury

But how will I say where will it break.

14. Jul 5, 2016

### Staff: Mentor

As rude man said, maybe it will never "break", but by writing the infinite series for the forces on each bead, I do see a place where there is the biggest difference in forces to the left and right in the string of beads...

15. Jul 5, 2016

### haruspex

that's not quite it. In considering whether it will break between the nth and the n+1th, it's the force between the first n, as a unit, and the rest that matters.

16. Jul 5, 2016

### haruspex

Coulomb's?

17. Jul 5, 2016

### Ankit Chowdhury

Yes that's a spelling mistake