Two equally charged tiny spheres of mass 1.0 g are placed 2.0 cm apart.When released,they begin to accelerate away from each other at
What is the magnitude of the charge on each sphere,assuming only that the electric force is present? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Question

Two equally charged tiny spheres of mass 1.0 g are placed 2.0 cm apart.When released,they begin to accelerate away from each other at

What is the magnitude of the charge on each sphere,assuming only that the electric force is present? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Quizplus · Accepted Answer

First, we can calculate the force between the two charged spheres using the formula:

F = k(q1q2/r^2)

where F is the force, k is the Coulomb constant, q1 and q2 are the charges on the spheres, and r is the distance between the centers of the spheres. Since the spheres are accelerating away from each other, we know that the net force on each sphere is:

F = ma

where m is the mass of each sphere and a is the acceleration.

Setting these two equations equal to each other and solving for q1 and q2, we get:

q1 = q2 = (ma)(r^2)/k

Plugging in the given values, we get:

q1 = q2 = (0.001 kg)(11 m/s^2)(0.02 m)^2/(9.0 × 10^9 N · m^2/C^2)

q1 = q2 = 140 nC

Therefore, the magnitude of the charge on each sphere is 140 nC, which is option A.

Two Equally Charged Tiny Spheres of Mass 1