Understanding the Problem
In this scenario, two similar and equal charges repel each other with a force of 1.6 N when separated by a distance of 3 m. We need to find the strength of each charge using Coulomb's Law.
Coulomb's Law
Coulomb's Law states that the electrostatic force (F) between two charges (q1 and q2) is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance (r) between them. The formula is given by:
F = k * (|q1 * q2|) / r²
Where:
- F is the force between the charges (1.6 N)
- k is Coulomb's constant (approximately 8.99 x 10^9 N m²/C²)
- r is the distance between the charges (3 m)
- q1 and q2 are the magnitudes of the charges (equal in this case)
Calculating the Charge
Since both charges are equal (q1 = q2 = q), we can rewrite the formula as:
F = k * (q²) / r²
Now, substituting the known values:
1.6 N = (8.99 x 10^9 N m²/C² * q²) / (3 m)²
Rearranging the Formula
To find the charge (q), we rearrange the formula:
q² = (1.6 N * 9) / (8.99 x 10^9 N m²/C²)
Calculating q
Now, calculate q² and then take the square root:
- q² = (14.4) / (8.99 x 10^9)
- q = √(14.4 / (8.99 x 10^9))
Final Result
Perform this calculation to find the value of q, which will give you the strength of each charge.