Question

The particle P shown in figure (31-E11) has a mass of 10 mg and a charge of $-0.01\mu C.$ Each plate has a surface area $100c{m}^2$ on one side. What potential difference V should be applied to the combination to bold the particle P in equilibrium ?

Answer 1

Electrical force is balanced by the weight of the mass

$mg=qEE=$ electric field

or $mg=q\frac{V}{d}$

(where d = separation at the plates)

or $mg=q.V.\frac{V}{{\in }_{0}A}$

$(\because \frac{{\in }_{0}A}{d}=C\therefore \frac{1}{d}=\frac{C}{{\in }_{0}A})$

$V=\frac{mg{\in }_{0}A}{q.C}$

$=\frac{{10}^{-6}\times 9.8\times 8.88\times {10}^{-12}\times 100\times {10}^{-4}}{10\times {10}^{-8}\times 0.04\times {10}^{-6}}$

$V=43mV.$