A charged ball with a mass of m = 0.4 g is suspended in the air on a silk thread. From below, an opposite and equal

A charged ball with a mass of m = 0.4 g is suspended in the air on a silk thread. From below, an opposite and equal charge q is brought to it at a distance of r = 2.0 cm; as a result of this, the tension force of the thread T increases by n = 2.0 times. Find the amount of charge q.

Problem data: m (ball mass) = 0.4 g = 0.4 * 10 ^ -3 kg; r (distance between the ball and the supplied charge) = 2 cm = 0.02 m; T2 (final thread tension) = 2T1 (initial thread tension); q1 (ball charge) = q2 (applied charge) = q.

Constants: g (acceleration due to gravity) ≈ 10 m / s2; k (aspect ratio) = 9 * 10 ^ 9 m / F.

1) Projection of forces on the vertical axis before the charge is applied: Ft = T1.

2) The projection of forces on the vertical axis after the charge is applied: Fт – Т2 + Fк = 0.

m * g – 2T1 + k * q ^ 2 / r ^ 2 = 0.

m * g – 2m * g + k * q ^ 2 / r ^ 2 = 0.

k * q ^ 2 / r ^ 2 = m * g.

q = √ (m * g * r ^ 2 / k) = √ (0.4 * 10 ^ -3 * 10 * 0.02 ^ 2 / (9 * 10 ^ 9)) = 1.33 * 10 ^ – 8 cl.

Answer: The amount of charge is 1.33 * 10 ^ -8 C.