Posted by **Sandhya** on Saturday, February 6, 2010 at 6:45pm.

A thin insulating thread of length L is attached to a point on the perimeter of a thin disk.

Disk is has radius R< L and is charged with a uniform surface density, σ>0. At the end of

the thread there is a small ball mass m and charge q>0. The mass happens to be located

on disk's axis. What is the mass of the ball?

- Physics -
**bobpursley**, Saturday, February 6, 2010 at 7:02pm
Figure the Electric field from the charged disk along the axis at a distance z, given R

http://hyperphysics.phy-astr.gsu.edu/HBASE/electric/elelin.html#c3

Now, given that expression, then you know from the geometry with the angle theta the string makes from disk,

tanTheta=Eq/mg

But CosineTheta=R/L

and sinTheta=sqrt((L^2-R^2)/L^2) or

sinTheta=sqrt(1-(R/L)^2)

but sinTheta/cosTheta= tan Theta, so

Eq/mg=sqrt(1-(R/L)^2) *L/R

Eq/mg=sqrt((L/R)^2-1)

and now you can solve for L

Remember in your E expression, z=Sqrt(L^2-R^2)

As you can tell, some algebra will be required. Get a nice pad of paper.

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