two positively charged sphere have combined charged of 0.5microcolumb and repulsive force of 1.0newton and it's distance separation is2.0meter.what is the charge of each spheres?
well, F = k * q1*q2/d^2
so, plug in your numbers to find q1 and q2. Are they the same? They need not be.
To find the charge of each sphere, we can use Coulomb's Law, which states that the magnitude of the electrostatic force between two charged objects is directly proportional to the product of the 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 electrostatic force,
k is the Coulomb's constant (9.0 x 10^9 Nm^2/C^2),
q1 and q2 are the charges of the spheres, and
r is the distance separation between the spheres.
In this case, we are given:
F = 1.0 Newton
r = 2.0 meters
The combined charge of the spheres is given as 0.5 microcoulomb, which is equivalent to 0.5 x 10^-6 C.
We can rearrange the formula to solve for q1 or q2:
q1 * q2 = (F * r^2) / k
Substituting the given values:
q1 * q2 = (1.0 N * (2.0 m)^2) / (9.0 x 10^9 Nm^2/C^2)
q1 * q2 = (1.0 N * 4.0 m^2) / (9.0 x 10^9 Nm^2/C^2)
q1 * q2 = 4.0 Nm^2 / (9.0 x 10^9 Nm^2/C^2)
Now, to find the charge of each sphere, we need to divide the combined charge of 0.5 microcoulomb equally between them. So, we can consider q1 = q2 = x, where x is the charge of each sphere.
The equation becomes:
x * x = 4.0 Nm^2 / (9.0 x 10^9 Nm^2/C^2)
x^2 = 4.0 / (9.0 x 10^9) C^2
x = √(4.0 / (9.0 x 10^9)) C
Calculating the value:
x ≈ 1.333 x 10^-9 C
Therefore, the charge of each sphere is approximately 1.333 nanoCoulomb.