Question

одинаковые по модулю,но разные со знаком заряды 18 нКл розтавлены в двух вершинах равностаронего треугольника с стороной 2м.найти напрежонность эликтрического поля в третей вершине триугольника

Answer 1

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Answer 2

To find the electric field intensity at the third vertex of an equilateral triangle with side length 2m, where two charges of 18nC each are placed at two vertices, we can use the principle of superposition. The electric field intensity at a point due to multiple charges is the vector sum of the electric field intensities produced by each individual charge.

Let's denote the charges as Q1 and Q2, both having a magnitude of 18nC. Since the charges are equal in magnitude but opposite in sign, the net charge of the system is zero.

Electric Field Intensity at the Third Vertex:

To find the electric field intensity at the third vertex, we need to calculate the electric field intensity produced by each charge at that point and then add them vectorially.

Let's assume that the charges are placed at vertices A and B, and we want to find the electric field intensity at vertex C.

1. Electric Field Intensity due to Charge Q1 at Vertex C: The electric field intensity at vertex C due to charge Q1 can be calculated using Coulomb's law:

Electric Field Intensity at C due to Q1 = (k * |Q1|) / r^2

Where: - k is the electrostatic constant (k = 9 * 10^9 Nm^2/C^2) - |Q1| is the magnitude of charge Q1 (|Q1| = 18nC = 18 * 10^-9 C) - r is the distance between charge Q1 and vertex C (r = 2m)

2. Electric Field Intensity due to Charge Q2 at Vertex C: Similarly, the electric field intensity at vertex C due to charge Q2 can be calculated using Coulomb's law:

Electric Field Intensity at C due to Q2 = (k * |Q2|) / r^2

Where: - |Q2| is the magnitude of charge Q2 (|Q2| = 18nC = 18 * 10^-9 C) - r is the distance between charge Q2 and vertex C (r = 2m)

3. Vector Sum of Electric Field Intensities: To find the net electric field intensity at vertex C, we need to add the electric field intensities due to Q1 and Q2 vectorially. Since the charges are placed at the vertices of an equilateral triangle, the electric field intensities will have the same magnitude but different directions.

The direction of the electric field intensity at vertex C due to Q1 will be towards Q1, and the direction of the electric field intensity at vertex C due to Q2 will be towards Q2. The net electric field intensity at vertex C will be the vector sum of these two electric field intensities.

Calculation:

Let's calculate the electric field intensity at the third vertex of the equilateral triangle.

1. Electric Field Intensity due to Q1 at C: Electric Field Intensity at C due to Q1 = (9 * 10^9 Nm^2/C^2 * 18 * 10^-9 C) / (2m)^2

2. Electric Field Intensity due to Q2 at C: Electric Field Intensity at C due to Q2 = (9 * 10^9 Nm^2/C^2 * 18 * 10^-9 C) / (2m)^2

3. Vector Sum of Electric Field Intensities: The net electric field intensity at vertex C will be the vector sum of the electric field intensities due to Q1 and Q2. Since the charges are equal in magnitude but opposite in sign, the net charge of the system is zero. Therefore, the net electric field intensity at vertex C will be zero.

Hence, the electric field intensity at the third vertex of the equilateral triangle is zero.

Please note that the above calculations assume that the charges are point charges and the distances are measured from the center of the charges to the vertex of the triangle.