Question

Два шарика радиусом 0,4 см и массой 0,2 г подвешены на нитях длиной 10 см так, что они в незаряженном состоянии соприкасаются. До какого потенциала были заряжены шарики, если они разошлись на угол 60 градусов.

Answer 1

0,4*0,2+10-60 и всё просто и легко

Answer 2

Calculation of the Charge on the Spheres

To determine the charge on the spheres, we can use the principle of electrostatic equilibrium. In this case, the spheres are initially in contact and then separated by an angle of 60 degrees. The length of the strings is given as 10 cm, and the radii of the spheres are 0.4 cm.

Let's assume that the charge on each sphere is q. Since the spheres are initially in contact, the total charge on both spheres is 2q.

When the spheres are separated, they reach an equilibrium position where the electrostatic forces acting on them are balanced. At this point, the tension in the strings provides the necessary centripetal force to keep the spheres in circular motion.

The electrostatic force between the spheres can be calculated using Coulomb's law:

F = k * (q^2) / r^2

Where: - F is the electrostatic force between the spheres, - k is the electrostatic constant (approximately 9 x 10^9 Nm^2/C^2), - q is the charge on each sphere, and - r is the distance between the centers of the spheres.

In this case, the distance between the centers of the spheres can be calculated using the given length of the strings and the angle between them. Using basic trigonometry, we can find that the distance between the centers of the spheres is approximately 0.173 cm.

Now, we can equate the electrostatic force to the centripetal force:

F = m * (v^2) / r

Where: - m is the mass of each sphere (given as 0.2 g, which is equal to 0.0002 kg), - v is the velocity of the spheres, and - r is the distance between the centers of the spheres.

Since the spheres are in circular motion, the velocity can be calculated using the angular velocity:

v = r * ω

Where: - ω is the angular velocity of the spheres.

The angular velocity can be calculated using the time period of the circular motion:

ω = 2π / T

Where: - T is the time period of the circular motion.

The time period can be calculated using the given length of the strings and the acceleration due to gravity:

T = 2π * √(L / g)

Where: - L is the length of the strings (given as 10 cm, which is equal to 0.1 m), and - g is the acceleration due to gravity (approximately 9.8 m/s^2).

Now, we can substitute the expressions for velocity and time period into the equation for the centripetal force:

F = m * (r * ω)^2 / r

Simplifying the equation, we get:

F = m * r * ω^2

Equating the electrostatic force and the centripetal force, we have:

k * (q^2) / r^2 = m * r * ω^2

Substituting the expressions for the angular velocity and the distance between the centers of the spheres, we get:

k * (q^2) / r^2 = m * r * (2π / T)^2

Now, we can substitute the expressions for the time period and the distance between the centers of the spheres, and solve for the charge on each sphere:

k * (q^2) / (0.173^2) = 0.0002 * 0.173 * (2π / √(0.1 / 9.8))^2

Simplifying the equation, we find:

q^2 = (0.0002 * 0.173 * (2π / √(0.1 / 9.8))^2) * (0.173^2) / k

Taking the square root of both sides, we can find the charge on each sphere:

q = √((0.0002 * 0.173 * (2π / √(0.1 / 9.8))^2) * (0.173^2) / k)

Now, let's calculate the value of q using the given values and the above equation.

Calculation:

Using the given values: - m = 0.0002 kg - r = 0.173 cm = 0.00173 m - L = 0.1 m - g = 9.8 m/s^2 - k = 9 x 10^9 Nm^2/C^2

Substituting these values into the equation, we find:

q = √((0.0002 * 0.00173 * (2π / √(0.1 / 9.8))^2) * (0.00173^2) / (9 x 10^9))

Calculating this expression, we find that the charge on each sphere is approximately 1.39 x 10^-9 C.

Therefore, the spheres were charged to a potential of approximately 1.39 x 10^-9 C before they separated and moved to an angle of 60 degrees.

Please note that the above calculation assumes ideal conditions and neglects any other factors that may affect the system.