Two identical positively charged balls have the same masses m1 = m2 = 0.23kg and are located at a distance

| March 9, 2021 | education

Two identical positively charged balls have the same masses m1 = m2 = 0.23kg and are located at a distance significantly exceeding their radii. The charge of one of the balls is q1 = 11C. Find the charge of another ball q2 if the Coulomb force is compensated by the force of gravitational interaction.

To find out the required charge of the second ball, consider the equality: k * q1 * qx / r ^ 2 = Fk (Coulomb force) = Fgr (gravitational force) = G * m1 * m2 / r ^ 2 = G * m2 / r ^ 2 , whence we express: qx = r ^ 2 * G * m ^ 2 / (r2 * k * q1) = G * m ^ 2 / (k * q1).

Const: G – gravitational constant (G ≈ 6.67 * 10 ^ -11 m2 / (s2 * kg)); k – coefficient of proportionality (k = 9 * 10 ^ 9 N * m2 / Cl2).

Data: m is the mass of each charged ball (m = 0.23 kg); q1 – known charge of one of the balls (q1 = 11 C).

Let’s perform the calculation: qx = G * m ^ 2 / (k * q1) = 6.67 * 10 ^ -11 * 0.23 ^ 2 / (9 * 10 ^ 9 * 11) ≈ 3.564 * 10 ^ -23 Kl ( * if the known charge is 4 * 10 ^ -11 C, then the charge of the other ball: q2 ≈ 9.8 * 10 ^ -12 C).

Answer: The charge of the other ball is 3.564 * 10 ^ -23 C (* 9.8 * 10 ^ -12 C).



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