Two identical charged balls, each weighing 0.5 g and suspended on threads 1 m

Two identical charged balls, each weighing 0.5 g and suspended on threads 1 m long, were separated by 4 cm from each other. find the charge of each ball.

To find out the charge of each of the indicated balls, we project the acting forces onto the horizontal axis: Fк – T * sinα = 0 = k * q ^ 2 / r ^ 2 – m * g / cosα * sinα = k * q ^ 2 / r ^ 2 – m * g * tgα = k * q ^ 2 / r ^ 2 – m * g * (0.5r / √ (l ^ 2 – (0.5r) ^ 2)), whence we express: q = √ (m * g * (0.5r / √ (l ^ 2 – (0.5r) ^ 2)) * r ^ 2 / k).

Const: g – gravitational acceleration (let’s take g ≈ 9.81 m / s2); k – coeff. proportionality (k = 9 * 10 ^ 9 N * m2 / C).

Data: m is the mass of the ball (m = 0.5 g = 5 * 10 ^ -4 kg); r is the distance between the balls (r = 4 cm = 0.04 m); l is the length of the thread (l = 1 m).

Let’s calculate: q = √ (m * g * (0.5r / √ (l ^ 2 – (0.5r) ^ 2)) * r ^ 2 / k) = √ (5 * 10 ^ -4 * 9, 81 * (0.5 * 0.04 / √ (12 – (0.5 * 0.04) ^ 2)) * 0.042 / (9 * 10 ^ 9)) ≈ 4.18 * 10 ^ -9 C = 4.18 nC.

Answer: The charge of each of the indicated balls should be 4.18 nC.