two small spheres lie 1.5 meters apart and carry identical charges. How large is the charge on each if a sphere experiences a force of 2.0 N.
To determine the charge on each sphere, we can use Coulomb's Law, which states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is:
F = k * (q1 * q2) / r^2
Where:
- F is the force between the spheres (given as 2.0 N)
- k is the Coulomb's constant (approximately 9 x 10^9 N.m^2/C^2)
- q1 and q2 are the charges on the spheres (which we want to find)
- r is the distance between the spheres (given as 1.5 meters)
Rearranging the formula, we can solve for q1 or q2:
q1 * q2 = (F * r^2) / k
Since the spheres carry identical charges, q1 = q2 = q (let's call it q).
Therefore, the equation becomes:
q^2 = (F * r^2) / k
To find the value of q, we can plug in the known values:
q^2 = (2.0 N * (1.5 meters)^2) / (9 x 10^9 N.m^2/C^2)
Solving this equation will give us the charge magnitude on each sphere.
Calculating the equation:
q^2 = (2.0 N * (1.5 meters)^2) / (9 x 10^9 N.m^2/C^2)
q^2 = (2.0 N * 2.25 meters^2) / (9 x 10^9 N.m^2/C^2)
q^2 = (2.0 N * 2.25 meters^2) / (9 x 10^9 N.m^2/C^2)
q^2 = 4.5 N.m^2 / (9 x 10^9 N.m^2/C^2)
q^2 = 5 x 10^-10 C^2 / (9 x 10^9 N.m^2/C^2)
q^2 ≈ 5.56 x 10^-20 C^2 / N.m^2
To find the value of q, we can take the square root of both sides:
q ≈ √(5.56 x 10^-20 C^2 / N.m^2)
Calculating the square root:
q ≈ 7.46 x 10^-10 C
Hence, the magnitude of the charge on each sphere is approximately 7.46 x 10^-10 Coulombs.