Question

If a small sphere of mass $m$ and charge $q$ is hanged from a silk thread at an angle $\theta $ with the surface of a vertical charged conducting plate, then for equilibrium of sphere the surface charge density of the plate -

• A. $\frac{\epsilon _{0} m g t a n \theta }{q}$
• B. $\frac{2 \epsilon _{0} m g t a n \theta }{q}$
• C. $\epsilon _{0}mgqtan\theta $
• D. $\frac{\epsilon _{0} m g t a n \theta }{3 q}$

Answer 1

Answer: (A)

$T \, sin \, \theta \, = \, qE\ldots \left(\right.1\left.\right)$
$T \, cos \, \theta \, = \, mg\ldots \left(\right.2\left.\right)$
$tan \, \theta = \, \frac{q \, E}{m g} \, = \, \frac{q \, \sigma }{\epsilon _{0} m g}$
$\sigma \, = \, \frac{\epsilon _{0} m g t a n \theta }{q}$