2. PROBLEM. The triangle has equal lateral sides of 8 cm, there are charges q1,92 in two low vertexes. q1=q2=2nC Find the force F acting on a charge of 1 nC placed at the high vertex of the triangle. Angle at the high vertex 120^circ

To solve this problem, we can use Coulomb's law, which states that the force between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.<br /><br />Given information:<br />- The triangle has equal lateral sides of 8 cm.<br />- There are charges q1 and q2 placed at the two low vertices of the triangle, with q1 = q2 = 2 nC.<br />- A charge of 1 nC is placed at the high vertex of the triangle.<br />- The angle at the high vertex is 120 degrees.<br /><br />Step 1: Calculate the distance between the high vertex and the low vertices.<br />Since the triangle is equilateral, the distance between the high vertex and the low vertices is equal to the side length of the triangle, which is 8 cm.<br /><br />Step 2: Calculate the force between the charge at the high vertex and the charge at one of the low vertices.<br />Using Coulomb's law, the force between the charge at the high vertex and the charge at one of the low vertices is given by:<br />F = k * (q1 * q2) / r^2<br />where k is the Coulomb constant (k = 8.99 × 10^9 N⋅m^2/C^2), q1 and q2 are the charges, and r is the distance between them.<br /><br />Substituting the values, we get:<br />F = (8.99 × 10^9 N⋅m^2/C^2) * (2 × 10^-9 C) * (2 × 10^-9 C) / (0.08 m)^2<br />F = 2.2475 × 10^-3 N<br /><br />Step 3: Calculate the force between the charge at the high vertex and the charge at the other low vertex.<br />Since the angle at the high vertex is 120 degrees, the force between the charge at the high vertex and the charge at the other low vertex will have the same magnitude as the force between the charge at the high vertex and the charge at one of the low vertices, but it will be directed in the opposite direction.<br /><br />Therefore, the force between the charge at the high vertex and the charge at the other low vertex is also 2.2475 × 10^-3 N.<br /><br />Step 4: Calculate the net force acting on the charge at the high vertex.<br />The net force acting on the charge at the high vertex is the vector sum of the forces from the two low vertices.<br /><br />Since the forces are equal in magnitude and opposite in direction, the net force is zero.<br /><br />Therefore, the force F acting on the charge of 1 nC placed at the high vertex of the triangle is 0 N.