If the number of electric lines of force emerging out of a closed surfsace is 1000, then the charge enclosed by the surface is

Options

A. `8.854xx10^(-9)` C
B. `8.854xx10^(-4)` C
C. `8.854xx10^(-1)` C
D. 8.854 C

Answer

To find the charge enclosed by a closed surface when the number of electric lines of force emerging from it is given, we can use Gauss's law. Here's a step-by-step solution:

### Step 1: Understand the relationship between electric lines of force and electric flux
The number of electric lines of force emerging from a closed surface is equal to the electric flux (\( \Phi_E \)) through that surface. Therefore, if there are 1000 electric lines of force, we can say:
\[ \Phi_E = 1000 \]

### Step 2: Apply Gauss's Law
According to Gauss's law, the electric flux through a closed surface is related to the charge (\( q \)) enclosed by that surface:
\[ \Phi_E = \frac{q}{\epsilon_0} \]
where \( \epsilon_0 \) is the permittivity of free space, approximately equal to \( 8.85 \times 10^{-12} \, \text{C}^2/\text{N m}^2 \).

### Step 3: Rearrange the equation to find the enclosed charge
From the equation above, we can rearrange it to solve for the charge \( q \):
\[ q = \Phi_E \cdot \epsilon_0 \]

### Step 4: Substitute the known values
Now substitute the values we have:
\[ q = 1000 \cdot (8.85 \times 10^{-12} \, \text{C}^2/\text{N m}^2) \]

### Step 5: Calculate the charge
Now, perform the multiplication:
\[ q = 1000 \cdot 8.85 \times 10^{-12} = 8.85 \times 10^{-9} \, \text{C} \]

### Final Answer
Thus, the charge enclosed by the surface is:
\[ \boxed{8.85 \times 10^{-9} \, \text{C}} \]