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 (a), (b), (c), and (d), we need to use the equations related to electric field, electrostatic force, and gravitational force.
(a) To find the magnitude of the electric field (E), we use the equation:
E = F / q
Where E is the electric field, F is the electrostatic force, and q is the charge. Given that F = 4.3 x 10^(-6) N and q = -2.1 x 10^(-9) C, we can substitute these values into the equation:
E = (4.3 x 10^(-6) N) / (-2.1 x 10^(-9) C)
Evaluating this expression will give us the magnitude of the electric field.
(b) To find the magnitude of the electrostatic force (Fp) on a proton, we use the equation:
Fp = Eq
Where Fp is the electrostatic force, E is the electric field, and q is the charge of the proton. Since the charge of a proton is 1.6 x 10^(-19) C, we can use this value along with the magnitude of the electric field obtained in part (a) to calculate the electrostatic force.
Fp = (electric field magnitude) * (1.6 x 10^(-19) C)
(c) To find the gravitational force (Fg) on the proton, we use the equation:
Fg = mg
Where Fg is the gravitational force, m is the mass of the proton, and g is the acceleration due to gravity. The mass of a proton is approximately 1.67 x 10^(-27) kg and the acceleration due to gravity is approximately 9.8 m/s^2. Plugging in these values into the equation will give us the gravitational force.
Fg = (1.67 x 10^(-27) kg) * (9.8 m/s^2)
(d) To find the ratio of the electrostatic force to the gravitational force, we divide the magnitude of the electrostatic force (obtained in part (b)) by the magnitude of the gravitational force (obtained in part (c)).
Ratio = (Fp) / (Fg)
Evaluate the ratio to obtain the final answer.
By following these steps and performing the necessary calculations, you will find the answers to parts (a), (b), (c), and (d) of the question.