# Force due to a line charge

1. Feb 16, 2008

### lat3ralus65

1. The problem statement, all variables and given/known data
A 10-cm long thin glass rod is uniformly charged to +50 nC. A small plastic bead, charged to - 5.2 nC, is 4.1 cm from the center of the rod. What is the magnitude of the force on the bead?

2. Relevant equations
dF = (k dq)/r$$^{2}$$

3. The attempt at a solution
I've gotten to this point:

dF sin $$\theta$$ = k$$\lambda$$ * (dx/(h$$^{2}$$ + x$$^{2}$$)$$^{3/2}$$) * (h/$$\sqrt{h^{2} + x^{2}}$$)

and I understand fairly well how and why. But now I have no idea where to go from here, aside from the fact that I have to integrate at some point. I know the two halves of the rod are equivalent so I can integrate from 0 to 5 and double (right?).

What do I do? :grumpy:

2. Feb 17, 2008

### Hootenanny

Staff Emeritus
I'm not quite sure what you've done here as you haven't posted your initial steps. Furthermore, your initial equation should involve a distance element (dz), rather than a charge element (dq). The usual way to solve such problems is to consider the electric field

3. Feb 17, 2008

### marlon

Isn't he using the line charge concept ? I guess so : dq = pdz, where the p denotes the charge per unit of distance.

marlon

4. Feb 17, 2008

### Hootenanny

Staff Emeritus
Now you mention it, yes it does . I'll go and put another coffee on...