Why is the following situation impossible? Two identical dust particles of mass

Question

Why is the following situation impossible? Two identical dust particles of mass 1.00 µg are floating in empty space, far from any external sources of large gravitational or electric fields, and at rest with respect to each other. Both particles carry electric charges that are identical in magnitude and sign. The gravitational and electric forces between the particles happen to have the same magnitude, so each particle experiences zero net force and the distance between the particles remains constant.

Explanation / Answer

Because if the two forces are equal, we have Gm2/r2 = kq2/r2 or Gm2 = kq2.

Solving for q, q = (Gm2/k)1/2

= ((6.6738 * 10-11 m3/kg s2)(1.00 * 10-9 kg)2/(8.9876 * 109 Nm2/C2))1/2

= 8.617 * 10-20 C       but the smallest charge possible is the elementary charge of the electron or proton which is 1.602 * 10-19 C, so the quantity of charge is impossible.

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.