The intensity of electric field required to balance a proton of mass `1.7xx10^(-27)kg` and charge `1.6 xx 10^(-19) C` is nearly

Options

A. `1xx10^(-7)V//m`
B. `1xx10^(-5)V//m`
C. `1xx10^(7)V//m`
D. `1xx10^(5)V//m`

Explanation

To find the intensity of the electric field required to balance a proton, we need to set the electric force equal to the gravitational force acting on the proton. Here are the steps to solve the problem:

### Step 1: Identify the forces acting on the proton
The forces acting on the proton are:
- The gravitational force (weight) acting downward, given by \( F_g = mg \)
- The electric force acting upward, given by \( F_e = qE \)

### Step 2: Write the expressions for the forces
1. The gravitational force \( F_g \) can be calculated using:
\[ F_g = mg \]
where:
- \( m = 1.7 \times 10^{-27} \, \text{kg} \) (mass of the proton)
- \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity)

2. The electric force \( F_e \) can be expressed as:
\[ F_e = qE \]
where:
- \( q = 1.6 \times 10^{-19} \, \text{C} \) (charge of the proton)
- \( E \) is the electric field intensity we want to find.

### Step 3: Set the forces equal to each other
To balance the proton, we set the electric force equal to the gravitational force:
\[ qE = mg \]

### Step 4: Solve for the electric field \( E \)
Rearranging the equation gives us:
\[ E = \frac{mg}{q} \]

### Step 5: Substitute the values into the equation
Substituting the known values:
\[ E = \frac{(1.7 \times 10^{-27} \, \text{kg}) \times (9.8 \, \text{m/s}^2)}{1.6 \times 10^{-19} \, \text{C}} \]

### Step 6: Calculate the numerator
Calculating the numerator:
\[ 1.7 \times 10^{-27} \times 9.8 = 1.666 \times 10^{-26} \, \text{N} \]

### Step 7: Calculate the electric field \( E \)
Now, substituting back into the equation for \( E \):
\[ E = \frac{1.666 \times 10^{-26}}{1.6 \times 10^{-19}} = 1.04125 \times 10^{-7} \, \text{V/m} \]

### Step 8: Round the result
Rounding gives us:
\[ E \approx 1.04 \times 10^{-7} \, \text{V/m} \]

### Conclusion
The intensity of the electric field required to balance the proton is approximately \( 1.04 \times 10^{-7} \, \text{V/m} \).

---