Calculate the magnitude of the electric field which can just balance a deuteron of mass `3.2xx10^(-27) kg`

Explanation

To calculate the magnitude of the electric field that can just balance a deuteron of mass \(3.2 \times 10^{-27} \, \text{kg}\), we will follow these steps:

### Step 1: Identify the forces acting on the deuteron
The deuteron, which is a nucleus of deuterium, has a mass and a positive charge. The forces acting on it are:
- The gravitational force acting downward, given by \( F_g = mg \)
- The electric force acting upward, given by \( F_e = qE \)

### Step 2: Write the expression for gravitational force
The gravitational force \( F_g \) can be calculated using the formula:
\[ F_g = mg \]
Where:
- \( m = 3.2 \times 10^{-27} \, \text{kg} \) (mass of the deuteron)
- \( g \approx 10 \, \text{m/s}^2 \) (acceleration due to gravity)

### Step 3: Calculate the gravitational force
Substituting the values into the equation:
\[ F_g = (3.2 \times 10^{-27} \, \text{kg})(10 \, \text{m/s}^2) = 3.2 \times 10^{-26} \, \text{N} \]

### Step 4: Identify the charge of the deuteron
The charge \( q \) of a deuteron (which has one proton) is:
\[ q = 1.6 \times 10^{-19} \, \text{C} \]

### Step 5: Set up the balance of forces
For the deuteron to be in equilibrium, the upward electric force must balance the downward gravitational force:
\[ qE = mg \]

### Step 6: Solve for the electric field \( E \)
Rearranging the equation gives:
\[ E = \frac{mg}{q} \]

### Step 7: Substitute the values into the equation
Substituting the values we calculated:
\[ E = \frac{3.2 \times 10^{-26} \, \text{N}}{1.6 \times 10^{-19} \, \text{C}} \]

### Step 8: Calculate the electric field
Calculating the above expression:
\[ E = 2.0 \times 10^{-7} \, \text{V/m} \]

### Final Answer
The magnitude of the electric field that can just balance the deuteron is:
\[ E = 2.0 \times 10^{-7} \, \text{V/m} \]

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