The electric field that can balance a charged particle of mass `3.2xx10^(-27)`kg is (Given that the charge on the particle is `1.6xx10^(-19)C`)

Options

A. `19.6xx10^(-8)NC^(-1)`
B. `20xx10^(-6)NC^(-1)`
C. `19.6xx10^(8)NC^(-1)`
D. `20xx10^(6)NC^(-1)`

Explanation

To find the electric field that can balance a charged particle of mass \(3.2 \times 10^{-27}\) kg and charge \(1.6 \times 10^{-19}\) C, we can follow these steps:

### Step 1: Understand the Forces Acting on the Charged Particle
The charged particle experiences two forces: the gravitational force acting downward and the electric force acting upward. For the particle to be in equilibrium (balanced), these two forces must be equal in magnitude.

### Step 2: Calculate the Gravitational Force
The gravitational force \(F_g\) acting on the particle can be calculated using the formula:
\[ F_g = m \cdot g \]
where:
- \(m = 3.2 \times 10^{-27}\) kg (mass of the particle)
- \(g \approx 9.8 \, \text{m/s}^2\) (acceleration due to gravity)

Substituting the values:
\[ F_g = 3.2 \times 10^{-27} \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 3.136 \times 10^{-26} \, \text{N} \]

### Step 3: Set Up the Electric Force Equation
The electric force \(F_e\) acting on the charged particle is given by:
\[ F_e = E \cdot Q \]
where:
- \(E\) is the electric field strength (what we want to find)
- \(Q = 1.6 \times 10^{-19}\) C (charge of the particle)

### Step 4: Set the Forces Equal for Equilibrium
For the particle to be balanced, the electric force must equal the gravitational force:
\[ F_e = F_g \]
Substituting the expressions for \(F_e\) and \(F_g\):
\[ E \cdot Q = m \cdot g \]

### Step 5: Solve for the Electric Field \(E\)
Rearranging the equation to solve for \(E\):
\[ E = \frac{F_g}{Q} \]
Substituting the values we calculated:
\[ E = \frac{3.136 \times 10^{-26} \, \text{N}}{1.6 \times 10^{-19} \, \text{C}} \]

### Step 6: Calculate the Value of \(E\)
Now performing the calculation:
\[ E = 1.96 \times 10^{-7} \, \text{N/C} \]

### Final Answer
The electric field that can balance the charged particle is:
\[ E \approx 1.96 \times 10^{-7} \, \text{N/C} \]