Question

A water droplet of radius 0.018 mm remains stationary in the air.
If the downward-directed electric field of the Earth is 150 N/C, how many excess electron charges must the water droplet have?

Answer 1

Concepts and reason

The concepts used to solve this problem are electric force, electric field, density, and charge.

Use the radius to find the volume of the water droplet.

Use the density and volume to find the expression for the mass of the droplet.

Use the number of electrons and the magnitude of the electron charge to find the charge.

Use the mass and the acceleration due to gravity to find the expression for the force

Use the relation between the force and field to calculate the number of electrons that must have in water droplet.

Fundamentals

Expression for the charge is,

$q=ne $

Here, q is the charge, n is the number of electrons, and e is the electron charge.

Expression for the mass of the water droplet is,

$m=pV $

Here, m is the mass of the water, is the density of the water, and is the volume of the water droplet.

Expression for the volume of the water droplet is,

Here, V is the volume of the water droplet and R is the radius of the water droplet.

Expression for the force due to gravity is,

Here, F is the force due to gravity and g is the acceleration due to gravity.

Expression for the electric field is,

Here, E is the electric field.

Expression for the mass of the water droplet is,

$m=pV $

Substitute for V.

Expression for the force due to gravity is,

Substitute for m.

Expression for the electric field is,

Substitute for E and for q.

Rearrange the above equation to get the number of electronsthat must have in water droplet,

Expression for the number of electronsthat must have in water droplet is,

Substitute for , for R, for g, for E, and for e.

Ans:

The number of electronsthat must have in water droplet is.