The electric field near the surface of the earth is `300V//m`. The surface density of charge on the earth's surface is

Options

A. `3.65xx10^(-9)C//m^(2)`
B. `2.65xx10^(-9)C//m^(2)`
C. `3.65xx10^(9)C//m^(2)`
D. `2.65xx10^(-9)C//m^(2)`

Explanation

To solve the problem of finding the surface charge density on the Earth's surface given the electric field near the surface, we can follow these steps:

### Step 1: Understand the relationship between electric field and surface charge density
The electric field \( E \) near a charged surface is related to the surface charge density \( \sigma \) by the formula:

\[ E = \frac{\sigma}{\epsilon_0} \]

where \( \epsilon_0 \) is the permittivity of free space, approximately \( 8.85 \times 10^{-12} \, \text{C}^2/\text{N m}^2 \).

### Step 2: Rearrange the formula to find surface charge density
To find the surface charge density \( \sigma \), we can rearrange the formula:

\[ \sigma = E \cdot \epsilon_0 \]

### Step 3: Substitute the known values
We know that the electric field \( E \) is \( 300 \, \text{V/m} \). Now we can substitute the values into the equation:

\[ \sigma = 300 \, \text{V/m} \cdot 8.85 \times 10^{-12} \, \text{C}^2/\text{N m}^2 \]

### Step 4: Perform the calculation
Now we calculate \( \sigma \):

\[ \sigma = 300 \cdot 8.85 \times 10^{-12} = 2.655 \times 10^{-9} \, \text{C/m}^2 \]

### Step 5: Round the result
Rounding the result to three significant figures gives:

\[ \sigma \approx 2.65 \times 10^{-9} \, \text{C/m}^2 \]

### Final Answer
The surface charge density on the Earth's surface is approximately \( 2.65 \times 10^{-9} \, \text{C/m}^2 \).

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