Question

Two 0.50 gg spheres are charged equally and placed 2.5 cmcm apart. When released, they begin to accelerate at 170 m/s2m/s2 . What is the magnitude of thecharge on each sphere?

Answer 1

Answer:

q = 76.8*10⁻⁹ C = 76.8 nC

Explanation:

Assuming no other forces acting on the charges, and that both spheres must be considered as point charges (and as point masses as well) , the force that is responsible for the initial acceleration is the electrostatic force, which obeys Coulomb´s Law.

According to Newton´s 2nd Law, this force is related with the mass and the acceleration as follows:

$F = m*a = 0.0005 kg * 170 m/s2 = 0.085 N$

This same force, expressed as the electrostatic force, is as follows:

$F = \frac{k*q^{2}}{(.025m)^{2}}$

As both expressions for F are equal each other, we can solve for q:

$q =\sqrt{\frac{(.085N)*0.025 m2^{2}}{9*109} }$

⇒ q = 76.8*10⁻⁹ C = 76.8 nC