Two metallic spheres of mass 5 g each are charged equally and suspended with a silk string of length 40 cm. If the angle the strings make with the vertical is 37°, what is the charge on each sphere?
Ответы
Ответ: the charge on each sphere is approximately 1.6 microcoulombs.
Объяснение:
Let’s denote the charge on each sphere as q. The Coulomb’s law states that the electrostatic force between two charged objects is given by the formula F = k * q1 * q2 / r^2, where k is the Coulomb’s constant, q1 and q2 are the charges on the objects and r is the distance between them. Since the spheres are charged equally, we can write F = k * q^2 / r^2.
The weight of each sphere is given by W = m * g, where m is the mass of the sphere and g is the gravitational acceleration. Since the spheres are in equilibrium, the electrostatic force must be balanced by the horizontal component of the weight of each sphere. The horizontal component of the weight is given by W * sin(37°). Therefore, we can write:
k * q^2 / r^2 = W * sin(37°)
Substituting the known values, we get:
k * q^2 / (0.4 * sin(37°))^2 = 0.005 * 9.8 * sin(37°)
Solving for q, we get:
q = sqrt((0.4 * sin(37°))^2 * 0.005 * 9.8 * sin(37°) / k)
Since k = 8.99 * 10^9 N * m^2 / C^2, we get:
q ≈ 1.6 * 10^-6 C
Therefore, the charge on each sphere is approximately 1.6 microcoulombs.