A charged mass on the end of a light string is attached to a point on a uniformly charged vertical sheet of infinite extent. The acceleration of gravity is 9.8 m/s^2 and the permittivity of free space is 8.85 x 10^-12 C^2/Nm^2. Find the angle [tex] \theta [/tex] the thread makes with the vertically charge sheet. Answer in units of degrees.(adsbygoogle = window.adsbygoogle || []).push({});

Given:

mass of ball= 1 g

Areal charge density of the sheet= 0.23 [tex] \mu C/m^2[/tex]

length of the string = 78.9 cm

Then force of charge= qE= q[tex] \sigma [/tex] / 2E_0

We did some of this problem in class and went through the long process of drawing a free body diagram and summing up the components, we found that it was easier to use the pythagorean theorem to solve for T.

I found that T= [tex] \sqrt (mg)^2 + (qE)^2 [/tex]

So T= [tex] \sqrt 96.04 + 1.32 x 10^-5 [/tex]

So T= 9.8.

Then I plugged it into what we got for the forces in the y-direction, which was [tex] \theta= cos^-1 (-mg/T) [/tex]

So theta= cos ^-1 (-9.8/9.8)

= 180 degrees which is wrong... can someone help me please?

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# Homework Help: Charged mass on a string

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