Two identical charges are experiencing 200N repulsion force placed at 3cm distance . If both are connected and separated to same distance than force of repulsion on both charges are 225N . Then value of both charges are

To find the value of the identical charges based on the information provided, we can use Coulomb's Law, which describes the electrostatic force between two point charges. The law states that the force \( F \) between two charges \( q_1 \) and \( q_2 \) separated by a distance \( r \) is given by the formula:

Coulomb's Law

The formula is expressed as:

F = k * (|q1 * q2|) / r²

Where:

• F is the force between the charges (in Newtons).
• k is Coulomb's constant, approximately \( 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \).
• q1 and q2 are the magnitudes of the charges (in Coulombs).
• r is the distance between the charges (in meters).

Initial Setup

Initially, we have two identical charges, let's denote them as \( q \). The repulsion force between them is 200 N when they are 3 cm apart. First, we need to convert the distance into meters:

r = 3 cm = 0.03 m

Applying Coulomb's Law

Using Coulomb's Law for the initial scenario:

200 N = k * (q * q) / (0.03)²

Substituting the value of \( k \):

200 = (8.99 \times 10^9) * (q²) / (0.03)²

Now, let's solve for \( q² \):

200 = (8.99 \times 10^9) * (q²) / 0.0009

Multiplying both sides by 0.0009:

200 * 0.0009 = 8.99 \times 10^9 * q²

0.18 = 8.99 \times 10^9 * q²

Now, divide both sides by \( 8.99 \times 10^9 \):

q² = 0.18 / (8.99 \times 10^9)

q² ≈ 2.00 \times 10^{-11}

Taking the square root gives:

q ≈ 4.47 \times 10^{-6} \, \text{C}

Second Scenario

Now, when both charges are connected and then separated again to the same distance, the force of repulsion increases to 225 N. When the charges are connected, they share their charge equally. Thus, the new charge on each will be:

q' = q + q = 2q

Now, using Coulomb's Law again for the second scenario:

225 N = k * (q' * q') / (0.03)²

Substituting \( q' = 2q \):

225 = (8.99 \times 10^9) * (2q * 2q) / (0.03)²

225 = (8.99 \times 10^9) * (4q²) / (0.0009)

Multiplying both sides by 0.0009:

225 * 0.0009 = 8.99 \times 10^9 * 4q²

0.2025 = 8.99 \times 10^9 * 4q²

Dividing by \( 8.99 \times 10^9 \):

4q² = 0.2025 / (8.99 \times 10^9)

q² = 0.2025 / (4 * 8.99 \times 10^9)

q² ≈ 5.63 \times 10^{-12}

Taking the square root gives:

q ≈ 2.37 \times 10^{-6} \, \text{C}

Final Values

Thus, the value of each of the identical charges is approximately:

q ≈ 4.47 \times 10^{-6} \, \text{C} for the first scenario and q ≈ 2.37 \times 10^{-6} \, \text{C} for the second scenario after connecting and separating them.