Final answer:
To find the electrical force at the top corner of an equilateral triangle with sides of 18 cm and charges of -2.0 nC at each corner, we use Coulomb's law to calculate the force from each base charge and then apply vector addition considering the symmetry of the setup.
Step-by-step explanation:
The question asks us to calculate the magnitude of the electrical force exerted on a charged object located at the top corner of an equilateral triangle due to the two equally charged objects at its base. This problem involves an understanding of Coulomb's law, which states that the magnitude of the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Let's denote each charge by 'q' which is -2.0 nC (nanocoulombs), and the sides of the equilateral triangle by 'L' which is 18 cm. The force exerted by one charge at the base on the top charge is calculated using Coulomb's law: F = k * |q1 * q2| / d^2, where k is the Coulomb's constant (8.99 x 10^9 N*m^2/C^2), q1 and q2 are the charges and d is the distance between the charges. Because the triangle is equilateral, the distances are equal, so we use 18 cm or 0.18 m for 'L'. We must consider both forces from the base charges and use vector addition to find the resultant force as they are exerted in different directions. Since the triangle is equilateral, the forces are symmetrical, and thus their vertical components cancel out, leaving only the horizontal components that add up.
To find the total force on the top charge, we can simply double the horizontal component of one of the two identical forces (as their vertical components cancel out). By using trigonometry, we find that the horizontal component due to one charge is F * cos(60°), and hence the total horizontal force, F_total, will be 2 * F * cos(60°).