Two equal and like charges when placed 50m apart experience a repulsive force of 144N. The magnitude of charge in micro-coulomb will be:

To find the magnitude of the charges, we can use Coulomb's Law, which states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. The formula is given by:

Coulomb's Law Formula

F = k * (|q1 * q2|) / r²

Where:

• F = force between the charges (in Newtons)
• k = Coulomb's constant (approximately 8.99 x 10^9 N m²/C²)
• q1 and q2 = magnitudes of the charges (in Coulombs)
• r = distance between the charges (in meters)

Given Values

In this case:

• F = 144 N
• r = 50 m
• q1 = q2 = q (since the charges are equal)

Substituting Values

We can rewrite the formula as:

144 = (8.99 x 10^9) * (q²) / (50)²

Calculating the Charges

Now, rearranging the equation to solve for q:

q² = (144 * (50)²) / (8.99 x 10^9)

Calculating the right side:

q² = (144 * 2500) / (8.99 x 10^9) = 360000 / (8.99 x 10^9)

q² ≈ 4.0 x 10^-6

Taking the square root gives:

q ≈ 2.0 x 10^-3 C

Converting to Micro-Coulombs

To convert Coulombs to micro-Coulombs (1 C = 1,000,000 µC):

q ≈ 2.0 x 10^-3 C = 2000 µC

Final Answer

The magnitude of each charge is approximately 2000 micro-Coulombs.