A charged cloud system produces an electric field in the air near Earth's surface. A particle of charge -2.1 x 10-9 C is acted on by a downward electrostatic force of 4.3 x 10-6 N when placed in this field. (a) What is the magnitude of the electric field? (b) What is the magnitude of the electrostatic force on a proton placed in this field? (c) What is the gravitational force on the proton? (d) What is the ratio of the electrostatic force to the gravitational force in this case?

To find the answers to these questions, we can use the formulas related to electric field, electrostatic force, and gravitational force. Let's go step by step:

(a) To find the magnitude of the electric field, we can use the formula:

Electric field (E) = Electrostatic force (F) / Charge of the test particle (q)

Given:
Electrostatic force (F) = 4.3 x 10^(-6) N
Charge of the test particle (q) = -2.1 x 10^(-9) C

Using the formula, we can calculate the electric field (E):

E = F / q
E = (4.3 x 10^(-6)) / (-2.1 x 10^(-9))
E ≈ -2.04857 x 10^3 N/C

The magnitude of the electric field is the absolute value of this result, so the magnitude of the electric field is approximately 2.04857 x 10^3 N/C.

(b) To find the magnitude of the electrostatic force on a proton, we need to know the charge of a proton. The charge of a proton is +1.6 x 10^(-19) C.

Using the formula:

Electrostatic force (F) = Electric field (E) * Charge of the test particle (q)

We substitute the values:
E = -2.04857 x 10^3 N/C (from part a)
q = +1.6 x 10^(-19) C (charge of a proton)

F = E * q
F = (-2.04857 x 10^3) * (+1.6 x 10^(-19))
F ≈ -3.27771 x 10^(-16) N

The magnitude of the electrostatic force on a proton is the absolute value of this result, so the magnitude of the electrostatic force on a proton is approximately 3.27771 x 10^(-16) N.

(c) The gravitational force on a proton near Earth's surface can be calculated using the formula:

Gravitational force (Fg) = mass of the proton (m) * acceleration due to gravity (g)

The mass of a proton is approximately 1.67 x 10^(-27) kg, and the acceleration due to gravity on Earth is about 9.8 m/s^2.

Fg = m * g
Fg = (1.67 x 10^(-27)) * (9.8)
Fg ≈ 1.6396 x 10^(-26) N

The magnitude of the gravitational force on the proton is approximately 1.6396 x 10^(-26) N.

(d) Finally, to find the ratio of the electrostatic force to the gravitational force, we divide the magnitude of the electrostatic force (from part b) by the magnitude of the gravitational force (from part c):

Ratio = Magnitude of electrostatic force / Magnitude of gravitational force

Ratio = (3.27771 x 10^(-16)) / (1.6396 x 10^(-26))
Ratio ≈ 1.99502 x 10^10

Therefore, the ratio of the electrostatic force to the gravitational force in this case is approximately 1.99502 x 10^10.