Two charged particles having charge `2.0 xx 10^(-8)C`. Each are joined by an isolating string of length 1m and the system is kept on a smooth horizontal task. The tension in the string.

Options

A. `36 xx 10^(-6)N`
B. `3.6 xx 10^(-6)N`
C. `36 xx 10^(6)N`
D. `3.6 xx 10^(6)N`

Answer

To find the tension in the string connecting two charged particles, we can follow these steps:

### Step 1: Identify the given values
- Charge of each particle, \( q = 2.0 \times 10^{-8} \, \text{C} \)
- Distance between the charges, \( r = 1 \, \text{m} \)
- Coulomb's constant, \( k = 9.0 \times 10^9 \, \text{N m}^2/\text{C}^2 \)

### Step 2: Use Coulomb's Law to calculate the electrostatic force
Coulomb's Law states that the force \( F \) between two point charges is given by:
\[ F = k \frac{q_1 q_2}{r^2} \]
Since both charges are equal, we can substitute \( q_1 = q_2 = q \):
\[ F = k \frac{q^2}{r^2} \]

### Step 3: Substitute the values into the formula
Substituting the known values into the equation:
\[ F = 9.0 \times 10^9 \, \frac{(2.0 \times 10^{-8})^2}{(1)^2} \]

### Step 4: Calculate \( (2.0 \times 10^{-8})^2 \)
Calculating the square of the charge:
\[ (2.0 \times 10^{-8})^2 = 4.0 \times 10^{-16} \]

### Step 5: Substitute back into the force equation
Now substituting this value back into the force equation:
\[ F = 9.0 \times 10^9 \, \frac{4.0 \times 10^{-16}}{1} \]

### Step 6: Calculate the force
Calculating the force:
\[ F = 9.0 \times 10^9 \times 4.0 \times 10^{-16} = 3.6 \times 10^{-6} \, \text{N} \]

### Step 7: Conclusion
The tension in the string, which is equal to the electrostatic force between the two charged particles, is:
\[ T = 3.6 \times 10^{-6} \, \text{N} \]

### Final Answer
The tension in the string is approximately \( 3.6 \times 10^{-6} \, \text{N} \).

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