The electric field strength in N `C^(-1)` that is required to just prevent a water drop carrying a change `16 xx 10^(-19)` C from falling under gravity is (g = 9.8 m `s^(-2)` , the mass of water drop = 0.0016 g )

Options

A. `9.8 xx10^(-16)`
B. `9.8 xx10^(16)`
C. `9.8 xx10^(-13)`
D. `9.8 xx10^(13)`

Answer

To solve the problem of finding the electric field strength required to prevent a water drop from falling under gravity, we can follow these steps:

### Step 1: Understand the forces acting on the water drop
The water drop experiences two forces:
1. The gravitational force (weight) acting downwards, given by \( F_g = mg \).
2. The electric force acting upwards, given by \( F_e = qE \).

### Step 2: Write down the known values
- Charge of the water drop, \( q = 16 \times 10^{-19} \, \text{C} \)
- Mass of the water drop, \( m = 0.0016 \, \text{g} = 0.0016 \times 10^{-3} \, \text{kg} = 1.6 \times 10^{-6} \, \text{kg} \)
- Acceleration due to gravity, \( g = 9.8 \, \text{m/s}^2 \)

### Step 3: Calculate the gravitational force
Using the formula for gravitational force:
\[ F_g = mg \]
Substituting the values:
\[ F_g = (1.6 \times 10^{-6} \, \text{kg})(9.8 \, \text{m/s}^2) = 1.568 \times 10^{-5} \, \text{N} \]

### Step 4: Set the forces equal for equilibrium
For the drop to be in equilibrium (not falling), the electric force must equal the gravitational force:
\[ F_e = F_g \]
This gives us:
\[ qE = mg \]

### Step 5: Solve for the electric field strength \( E \)
Rearranging the equation:
\[ E = \frac{mg}{q} \]
Substituting the values we have:
\[ E = \frac{(1.6 \times 10^{-6} \, \text{kg})(9.8 \, \text{m/s}^2)}{16 \times 10^{-19} \, \text{C}} \]

### Step 6: Calculate \( E \)
Calculating the numerator:
\[ 1.6 \times 10^{-6} \times 9.8 = 1.568 \times 10^{-5} \]
Now substituting this into the equation for \( E \):
\[ E = \frac{1.568 \times 10^{-5}}{16 \times 10^{-19}} = \frac{1.568 \times 10^{-5}}{1.6 \times 10^{-18}} = 9.8 \times 10^{13} \, \text{N/C} \]

### Final Result
The electric field strength required to just prevent the water drop from falling is:
\[ E = 9.8 \times 10^{13} \, \text{N/C} \]