To solve the problem, we need to find the gravitational and electrostatic forces acting on a proton placed in the electric field produced by a charged cloud system. Let's break down the solution step by step.
### Step 1: Determine the Electric Field (E)
We know that the electrostatic force (F) acting on a charge (Q) in an electric field (E) is given by the equation:
\[ F = Q \cdot E \]
From the problem, we have:
- The charge of the particle \( Q = -2 \times 10^{-9} \, \text{C} \)
- The electrostatic force \( F = 3 \times 10^{-6} \, \text{N} \) (acting downward)
Using the above equation, we can rearrange it to find the electric field (E):
\[ E = \frac{F}{Q} \]
Substituting the values:
\[ E = \frac{3 \times 10^{-6} \, \text{N}}{-2 \times 10^{-9} \, \text{C}} \]
Calculating this gives:
\[ E = -1.5 \times 10^{3} \, \text{N/C} \]
### Step 2: Calculate the Electrostatic Force on the Proton
The charge of a proton \( Q_p \) is:
\[ Q_p = 1.6 \times 10^{-19} \, \text{C} \]
The electrostatic force \( F_{e} \) on the proton in the electric field is given by:
\[ F_{e} = Q_p \cdot E \]
Substituting the values:
\[ F_{e} = 1.6 \times 10^{-19} \, \text{C} \cdot (-1.5 \times 10^{3} \, \text{N/C}) \]
Calculating this gives:
\[ F_{e} = -2.4 \times 10^{-16} \, \text{N} \]
### Step 3: Calculate the Gravitational Force on the Proton
The gravitational force \( F_{g} \) acting on the proton can be calculated using:
\[ F_{g} = m_p \cdot g \]
Where:
- The mass of the proton \( m_p = 1.67 \times 10^{-27} \, \text{kg} \)
- The acceleration due to gravity \( g = 9.8 \, \text{m/s}^2 \)
Substituting the values:
\[ F_{g} = 1.67 \times 10^{-27} \, \text{kg} \cdot 9.8 \, \text{m/s}^2 \]
Calculating this gives:
\[ F_{g} = 1.64 \times 10^{-26} \, \text{N} \]
### Final Answers
- The electrostatic force on the proton is \( F_{e} = -2.4 \times 10^{-16} \, \text{N} \) (upward).
- The gravitational force on the proton is \( F_{g} = 1.64 \times 10^{-26} \, \text{N} \) (downward).
