Question

A charged dust particle of radius 5 × 10^-7 m is located in a horizontal electric field having an intensity of 6.28 × 10⁵ V/m. The surrounding medium is air with a coefficient of viscosity η = 1.6 × 10^-5 N-s/m². If the particle moves with a uniform horizontal speed of 0.02 m/s, the number of electrons on it is ______.

Options

• 10.00

• 20.00

• 30.00

• 40.00

Answer 1

A charged dust particle of radius 5 × 10^-7 m is located in a horizontal electric field having an intensity of 6.28 × 10⁵ V/m. The surrounding medium is air with a coefficient of viscosity η = 1.6 × 10^-5 N-s/m². If the particle moves with a uniform horizontal speed of 0.02 m/s, the number of electrons on it is 30.00.

Explanation:

Because the dust particle is moving horizontally with uniform velocity, it is in dynamic equilibrium, and the forces operating on the dust particle horizontally are electric force (qE) and viscous force (6πηρv).

So, qE = 6πηρv

or neE = 6πηρv [as q = ne]

or, `n = (6piηrν)/(eE)`

= `(6 xx 3.14 xx 1.6 xx 10^-5 xx 5 xx 10^-7 xx 0.02)/((1.6  xx 10^-19)(6.28 xx 10^5))`

≈ 30