Two small plastic spheres are given positive electrical charges. When they are 11.0cm apart, the repulsive force between them has magnitude 0.300N.
What is the charge on each sphere if one sphere has four times the charge of the other?
force=kqq/r^2 solve for q
1.588*10^-7
4.76*10^-7
To find the charge on each sphere, we can set up an equation using Coulomb's law.
Coulomb's law states that the magnitude of 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. Mathematically, it can be expressed as:
F = k * (q1 * q2) / r^2
Where:
F is the force between the spheres (0.300 N),
k is the Coulomb's constant,
q1 and q2 are the charges on the spheres, and
r is the distance between the spheres (11.0 cm).
Since one sphere has four times the charge of the other, we can express their charges as:
q1 = 4q, and
q2 = q, where q is some constant.
Plugging in these values and rearranging the equation, we have:
0.300 N = k * [(4q) * q] / (0.11 m)^2
To solve for q, we need to know the value of k. Coulomb's constant, denoted as k, is equal to 9 × 10^9 Nm^2/C^2.
Let's substitute the given values and calculate the charge on each sphere.
To solve this problem, we can use Coulomb's Law, which relates the force between two charged objects to their charges and the distance between them. The formula for Coulomb's Law is:
F = (k * q1 * q2) / r^2
Where:
F is the magnitude of the repulsive force
k is the electrostatic constant (k = 9.0 x 10^9 N m^2/C^2)
q1 and q2 are the charges on the spheres
r is the distance between the spheres
In this case, we know the magnitude of the force (F = 0.300 N) and the distance between the spheres (r = 11.0 cm = 0.11 m). We are asked to find the charges on each sphere.
Let's denote the charge on one sphere as q and the charge on the other sphere as 4q, since one sphere has four times the charge of the other.
Using Coulomb's Law, we can rewrite the equation as:
F = (k * q1 * q2) / r^2
0.300 N = (9.0 x 10^9 N m^2/C^2) * (q) * (4q) / (0.11 m)^2
Simplifying this equation gives us:
0.300 N = (36 * k * q^2) / (0.11 m)^2
Now we can solve for q. Rearranging the equation gives us:
q^2 = (0.300 N * (0.11 m)^2) / (36 * k)
Taking the square root of both sides yields:
q = sqrt((0.300 N * (0.11 m)^2) / (36 * k))
Now we can substitute the given values of all the constants:
k = 9.0 x 10^9 N m^2/C^2
Plugging in the values and solving for q:
q = sqrt((0.300 N * (0.11 m)^2) / (36 * (9.0 x 10^9 N m^2/C^2)))
q ≈ 2.25 x 10^-7 C
Therefore, the charge on the smaller sphere is approximately 2.25 x 10^-7 C, and the charge on the larger sphere is four times this value, or 4 * (2.25 x 10^-7 C) = 9.0 x 10^-7 C.