A charged cloud system produces an electric field in the air near the earth's surface. A particle of charge `-2xx10^(-9)` C is acted on by a downward electrostatic force of `3xx10^(-6)` N when placed in this field. The gravitational and electrostatic force, respectively, exerted on a proton placed in this field are

Options

A. `1.64xx10^(-26)N, 2.4xx10^(-16)` N
B. `1.64xx10^(-26)N, 1.5xx10^(3)` N
C. `1.56xx10^(-18)N, 2.4xx10^(-16)` N
D. `1.5xx10^(3)N, 2.4xx10^(-16)` N

Answer

To solve the problem, we need to find the gravitational and electrostatic forces acting on a proton placed in the electric field produced by the charged cloud system.

### Step 1: Calculate the Electric Field (E)

We know that the electrostatic force (F) acting on a charged particle in an electric field is given by:
\[ F = Q \cdot E \]
where:
- \( F \) is the electrostatic force,
- \( Q \) is the charge of the particle,
- \( E \) is the electric field strength.

From the problem, we have:
- \( F = 3 \times 10^{-6} \, \text{N} \)
- \( Q = -2 \times 10^{-9} \, \text{C} \)

Rearranging the formula to solve for \( E \):
\[ E = \frac{F}{Q} \]

Substituting the values:
\[ E = \frac{3 \times 10^{-6}}{-2 \times 10^{-9}} \]
\[ E = -1.5 \times 10^{3} \, \text{N/C} \]

The negative sign indicates the direction of the electric field is opposite to that of the force on the negative charge.

### Step 2: Calculate the Gravitational Force (Fg) on the Proton

The gravitational force acting on the proton can be calculated using:
\[ F_g = m \cdot g \]
where:
- \( m \) is the mass of the proton,
- \( g \) is the acceleration due to gravity (approximately \( 10 \, \text{m/s}^2 \)).

The mass of a proton is:
\[ m = 1.67 \times 10^{-27} \, \text{kg} \]

Substituting the values:
\[ F_g = 1.67 \times 10^{-27} \cdot 10 \]
\[ F_g = 1.67 \times 10^{-26} \, \text{N} \]

### Step 3: Calculate the Electrostatic Force (Fe) on the Proton

The electrostatic force acting on the proton can be calculated using:
\[ F_e = q \cdot E \]
where:
- \( q \) is the charge of the proton (approximately \( 1.6 \times 10^{-19} \, \text{C} \)),
- \( E \) is the electric field strength calculated in Step 1.

Substituting the values:
\[ F_e = 1.6 \times 10^{-19} \cdot 1.5 \times 10^{3} \]
\[ F_e = 2.4 \times 10^{-16} \, \text{N} \]

### Final Answers
- Gravitational Force on the proton: \( F_g \approx 1.67 \times 10^{-26} \, \text{N} \)
- Electrostatic Force on the proton: \( F_e \approx 2.4 \times 10^{-16} \, \text{N} \)

### Summary
The gravitational and electrostatic forces exerted on a proton placed in the electric field are approximately:
- Gravitational Force: \( 1.67 \times 10^{-26} \, \text{N} \)
- Electrostatic Force: \( 2.4 \times 10^{-16} \, \text{N} \)