Two tiny spheres carrying the same charge are 1.4 meters apart in a vacuum and experience an electrical repulsion of 9.6 N. What is their charge?
To find the charge of the tiny spheres, we can use Coulomb's Law, which relates the electrical force between two charged objects to their charges and the distance between them.
Coulomb's Law is expressed as:
F = k * (q1 * q2) / r^2
Where:
F is the electrical force between the charges,
k is the electrostatic constant (9 x 10^9 N*m^2/C^2),
q1 and q2 are the charges of the objects,
r is the distance between the charges.
In this case, the spheres are carrying the same charge and experience an electrical repulsion, which means they have the same sign (either positive or negative).
Let's assume the charge of each sphere is q, and the distance between them is r.
The electrical force is given as F = 9.6 N, and the distance between the spheres is r = 1.4 m.
Using Coulomb's Law, we can rewrite the equation to solve for the charge (q):
q^2 = (F * r^2) / k
Let's substitute the given values into the equation and solve for q:
q^2 = (9.6 N * (1.4 m)^2) / (9 x 10^9 N*m^2/C^2)
Simplifying the equation:
q^2 = (18.144 N*m^2) / (9 x 10^9 N*m^2/C^2)
q^2 = 2.016 x 10^-9 C^2
Taking the square root of both sides of the equation:
q = ±√(2.016 x 10^-9 C^2)
Since the spheres have the same charge, we take the positive value:
q ≈ +1.42 x 10^-5 C
Therefore, each tiny sphere has a charge of approximately 1.42 x 10^-5 C.