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

[Ankit Chowdhury]

Homework Statement

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.

 

[berkeman]

Homework Statement

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.

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

 

[rude man]

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

 

[Ankit Chowdhury]

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

 

[berkeman]

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

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?

 

[Ankit Chowdhury]

Wait let me upload the picture of the question.

 

[Ankit Chowdhury]

 

[Ankit Chowdhury]

See question no. 26

 

[berkeman]

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

 

[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.

 

[berkeman]

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.

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...

 

[Ankit Chowdhury]

OK thanks I will try it .

 

[Ankit Chowdhury]

But how will I say where will it break.

 

[berkeman]

But how will I say where will it break.

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...

 

[haruspex]

then write the equation for the forces on the 2nd bead and so on.

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

 

[haruspex]

column's law

Coulomb's?

 

[Ankit Chowdhury]

Yes that's a spelling mistake