Question

15. it is a cloudy day and the clouds are charged. there is a downward electrostatic force of 3 x 10-6n acting on a -2 x 10-9 c charge that sits in the electric field. a) what is the magnitude of the electric field? b) what is the magnitude and direction of the electrostatic force on a proton placed in this field? c) what is the gravitational force on the proton?

Answer 1

Step-by-step explanation:

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

F = q * E

where F is the force exerted on the charge, q is the charge, and E is the electric field.

Substituting the given values into the equation, we have:

3 x 10^-6 N = (-2 x 10^-9 C) * E

Solving for E, we get:

E = (3 x 10^-6 N) / (-2 x 10^-9 C)

E ≈ -1.5 x 10^3 N/C (magnitude)

The magnitude of the electric field is approximately 1.5 x 10^3 N/C.

(b) The electrostatic force on a proton can be calculated using the same equation:

F = q * E

For a proton, the charge is positive (+1.6 x 10^-19 C). Substituting this value and the magnitude of the electric field (1.5 x 10^3 N/C) into the equation, we have:

F = (1.6 x 10^-19 C) * (1.5 x 10^3 N/C)

F ≈ 2.4 x 10^-16 N

The magnitude of the electrostatic force on the proton is approximately 2.4 x 10^-16 N. Since the charge of the proton is positive, the direction of the force will be opposite to the electric field, which is upward.

(c) The gravitational force on the proton can be calculated using the equation:

F_gravity = m * g

where F_gravity 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. The acceleration due to gravity on Earth is approximately 9.8 m/s^2.

Substituting the values into the equation, we have:

F_gravity = (1.67 x 10^-27 kg) * (9.8 m/s^2)

F_gravity ≈ 1.64 x 10^-26 N

The magnitude of the gravitational force on the proton is approximately 1.64 x 10^-26 N. The direction of the gravitational force is downward.