Question

маленький шарик массой 0,5г и зарядом 33,4 нКл подвешен на нити. Какой заряд надо поднести к нему снизу на 10 см,чтобы сила натяжения нити уменьшилась вдвое?

Answer 1

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Answer 2

Calculation of the Required Charge

To determine the charge that needs to be brought to the small ball from below to reduce the tension force in the string by half, we can use the principle of electrostatics. The tension force in the string is directly related to the electric field created by the charges on the ball.

Let's denote the initial charge on the ball as q1 and the final charge that needs to be brought to the ball as q2. The tension force in the string is given by the equation:

F = q1 * E1 = q2 * E2

Where: - F is the tension force in the string, - E1 is the electric field created by the initial charge on the ball, - E2 is the electric field created by the final charge on the ball.

Since we want to reduce the tension force in the string by half, we can write:

F/2 = q1 * E1 = q2 * E2

Now, let's consider the electric field created by a point charge. The electric field at a distance r from a point charge Q is given by the equation:

E = k * Q / r^2

Where: - E is the electric field, - k is the electrostatic constant (approximately 9 * 10^9 Nm^2/C^2), - Q is the charge creating the electric field, - r is the distance from the charge.

In our case, the distance from the charge to the point where the additional charge is brought is 10 cm (0.1 m). Therefore, we can write:

E1 = k * q1 / r^2 E2 = k * q2 / r^2

Substituting these equations into the previous equation, we get:

(F/2) = (q1 * k * q1) / (r^2) = (q2 * k * q2) / (r^2)

Simplifying the equation, we find:

q2 = sqrt((F/2) * (r^2) / k)

Now, let's substitute the given values into the equation to calculate the required charge.

Given: - Mass of the small ball = 0.5 g = 0.0005 kg - Charge on the small ball = 33.4 nC = 33.4 * 10^-9 C - Distance from the charge to the point where the additional charge is brought = 10 cm = 0.1 m

Using the equation, we can calculate the required charge:

q2 = sqrt((F/2) * (r^2) / k) = sqrt((0.5 * 0.0005 * 9.8) / (2 * 0.1^2 * 9 * 10^9))

Calculating this expression, we find that the required charge to be brought to the small ball from below is approximately 1.06 nC.

Please note that the above calculation assumes that the small ball is a point charge and neglects any other charges or objects in the vicinity that may affect the electric field.