Four small dust grains with a mass m=0.1 mg each located

Four small dust particles with a mass of m = 0.1 mg each are located at the vertices of a square with side a = 1 cm. Each speck of dust was given the same charge Q = 1 nC and was given the opportunity to fly away under the influence of repulsive forces. It is necessary to determine the speed of dust grains at a large distance from each other.

To solve this problem, you can use Coulomb’s law, which states that the force of interaction between two point charges is proportional to their charges and inversely proportional to the square of the distance between them:

F = k * Q1 * Q2 / r^2,

where F is the interaction force, Q1 and Q2 are the charges of point particles, r is the distance between them, k is the Coulomb constant.

In this problem, all charges are equal to Q, so the force of interaction between two dust particles can be written as:

F = k * Q^2 / r^2.

Since all four dust grains have the same charges and are located at the vertices of the square, each of them will be at a distance r = a * sqrt(2) / 2 from the other two dust grains and at a distance r = a from the remaining dust grain. Therefore, the interaction force between two dust grains located at a distance a can be written as:

F = k * Q^2 / a^2.

Thus, the total force acting on each speck of dust is:

F_total = 2 * F_diagonal + 2 * F_side = 4 * k * Q^2 / a^2.

The force acting on each speck of dust causes them to accelerate and move in the opposite direction. Therefore, the speed of dust particles can be determined by knowing the time they were exposed to the force.

The distance between dust grains at a large distance can be considered infinitely large, which means that the force of interaction between them tends to zero, and the speed of each dust grain also tends to zero.

The Four Small Specks of Dust product is a digital product available for purchase in our Digital Product Store. This product contains a detailed solution to Problem 31014, which deals with charged particle interactions. To solve the problem, Coulomb's law is used and the interaction force between four charged dust particles with a mass of m = 0.1 mg each, located at the vertices of a square with side a = 1 cm, is calculated. All dust grains have the same charge Q = 1 nC and can fly apart under the influence of repulsive forces.

The solution to the problem is presented in HTML format, designed in accordance with modern design requirements. You can easily read and study the solution to the problem, as it is presented in a convenient and understandable manner. Our digital goods store guarantees the quality of the product and can guarantee its effectiveness in solving problems related to the interaction of charged particles. Buy this product and get a unique solution to problem 31014, which will help you better understand the physical processes associated with electrostatics.

The product "Four Small Specks of Dust" contains a detailed solution to problem 31014, related to the interaction of charged particles. In this problem, four small dust particles with a mass of m = 0.1 mg each are located at the vertices of a square with side a = 1 cm. Each speck of dust was given the same charge Q = 1 nC and was given the opportunity to fly away under the influence of repulsive forces.

To solve this problem, Coulomb's law is used, which states that the force of interaction between two point charges is proportional to their charges and inversely proportional to the square of the distance between them. Using the formula for the force of interaction of charges, you can determine the total force acting on each grain of dust, which is equal to 4 * k * Q^2 / a^2.

The force acting on each speck of dust causes them to accelerate and move in the opposite direction. The speed of dust particles can be determined by knowing the time they were exposed to the force. However, if we consider the distance between dust grains at a large distance from each other, then the force of interaction between them tends to zero, and the speed of each dust grain also tends to zero.

The solution to the problem is presented in HTML format, designed in accordance with modern design requirements. The solution to the problem contains brief notes on the conditions, formulas and laws used in the solution, the derivation of the calculation formula and the answer. If you have any questions about the solution, you can ask for help.

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As for problem 31014, to solve this problem it is necessary to use Coulomb's law, which describes the force of interaction between two point charges. According to this law, the force of interaction is proportional to the product of charges and inversely proportional to the square of the distance between charges.

Thus, for this problem, we can calculate the repulsive force between each pair of dust grains using the formula F = kq1q2/r^2, where k is the Coulomb constant, q1 and q2 are the charges of dust grains, r is the distance between dust grains. Coulomb constant value k = 910^9 Nm^2/Cl^2.

After calculating the force, you can apply the laws of motion and find the speed of dust grains at a large distance from each other. Due to the large number of calculations, I cannot provide a detailed solution within this answer, but I can help with the calculations if specific questions arise.

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