Question

A particle (m = 1.5g and q = 25nC) hangs from a silk thread that makes 32 degrees with a large, uniformly charged non-conducting slab. Find the charge density (sigma) of the slab.

http://www.wellesley.edu/Physics/phyllisflemingphysics/108_p_electric_images/figure_for22.gif

Answer 1

Was able to use gravity to find tension in the single, and use the angle given to find tension along the x-axis, which had to be equivalent to the Electrostatic force on the particle if the particle is not in motion. From here, I divided by the charge of the particle to get the magnitude of electric field at that point (direction being along the x-axis).

this came out to:

\[E =(m_p / q_p )(g) \cot(\theta)\]

Unsure of how to utilize the E-field to solve for charge density on the plate.

Answer 2

Also, unsure if I can actually say that electrostatic force is equal to the tension in the string along the a-axis.

Answer 3

E for a slab = \[\frac{ \sigma }{ 2\epsilon _{0} }\]
\[ \sigma = 2\epsilon _{0} \frac{ mg }{q}\tan 32\]