The balls of the same name, located at a distance of 2m from each other, interact with a force of 1N.

| June 10, 2021 | education

The balls of the same name, located at a distance of 2m from each other, interact with a force of 1N. the total charge of the balls is 5 * 10 ^ 28 Cl. What is the smallest in modulus of the interacting charges?

Data: r is the distance between the presented balls (r = 2 m); Fк – force of interaction (Fк = 1 N); Q – total charge (Q = 5 * 10 ^ -5 C; * in the condition of inaccuracy).

Const: k – coefficient of proportionality (k = 9 * 10 ^ 9 N * m2 / Kl2).

Decision:

Coulomb force: Fk = k * q1 * q2 / r ^ 2 = k * q1 * (Q – q1) / r ^ 2 = k * (q1 * Q – q1 ^ 2) / r ^ 2.

Quadratic equation: q1 ^ 2 – q1 * Q + Fk * r ^ 2 / k = 0.

q1 ^ 2 – q1 * 5 * 10 ^ -5 + 1 * 2 ^ 2 / (9 * 10 ^ 9) = 0.

q1 ^ 2 – 5 * 10 ^ -5 * q1 + 0.44 (4) * 10 ^ -9 = 0.

The roots of the equation (charges of the presented balls): q1 ≈ 1.156 * 10 ^ -5 C and q2 ≈ 3.844 * 10 ^ -5 C.

Answer: The smaller charge, according to the calculation, is 1.156 * 10 ^ -5 C.



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