Force on a Charged Bead Near a Line Charge

[lat3ralus65]

Homework Statement

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?

Homework Equations

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

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:

 

[Hootenanny]

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 http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elelin.html#c1"

 

[marlon]

Furthermore, your initial equation should involve a distance element (dz), rather than a charge element (dq).

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


marlon

 

[Hootenanny]

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


marlon

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