Question

A charged particle of mass 1.0 g is suspended through a silk thread of length 40 cm in a horizontal electric field of $4.0\times {10}^{4}N{C}^{-1}$ If the particle stays at a distance of 24 cm from the wall in equilibrium, find the charge on the particle.

Answer 1

The forces acts on mass here

$1$. The tension in the thread

$2$. mg weight of mass partica-downward

$3$. Electric core $F=Eq$ due to horizontal field

Let the angle between the thread and verticle be $\alpha$

Use sine law,

$T=\frac{mg}{\sin (90+\alpha )}=\frac{Eq}{\sin (18-\alpha )}$ $m={10}^{-3}kg$

$Eq=mg\left(\tan \alpha \right)$

$\theta =\frac{mg\tan \alpha }{E}$

The length of thread in $40$cm.