Around a point charge of 5 nC under the action of an electric force, a small negatively charged ball moves uniformly around the circumference. Determine what is the modulus of the ratio of the ball’s charge to its mass if the radius of the circle is 30 cm, and the angular velocity of rotation is 5 rad / s? Consider that other forces do not act on the ball.
To find the value of the modulus of the ratio of the charge of the considered ball to its mass, we use the equality: Fк (Coulomb force) = m * ac; k * qz * qsh / R ^ 2 = m * ω ^ 2 * R, whence we express: qsh / m = ω ^ 2 * R * R ^ 2 / (k * qz) = ω ^ 2 * R ^ 3 / ( k * qz).
Constants and variables: ω – angular velocity of the ball (ω = 5 rad / s); R is the radius of the circle, the distance between the charge and the ball (R = 30 cm = 0.3 m); k – coefficient of proportionality (k = 9 * 10 ^ 9 m / F); qs – point charge (qs = 5 nC = 5 * 10 ^ -9 C).
Let’s calculate: qsh / m = ω ^ 2 * R ^ 3 / (k * qz) = 5 ^ 2 * 0.3 ^ 3 / (9 * 10 ^ 9 * 5 * 10 ^ -9) = 0.015 C / kg …
Answer: The ratio of the charge of the indicated ball to its mass is 0.015 C / kg.
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