Answer :
Final answer:
To determine the value of q2 that keeps q3 in equilibrium, we apply Coulomb's Law, balancing the forces from q1 and q2 on q3. Through calculations, q2 is found to be -4.00. The correct option is (c).
Explanation:
To solve the problem, we need to understand the principle of electric force equilibrium and apply Coulomb's Law, which states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. In this case, we are finding the value of q2 that makes q3 in equilibrium, meaning the net force acting on q3 due to q1 and q2 is zero.
Let's denote the forces acting on q3 due to q1 and q2 as F31 and F32, respectively. According to Coulomb's Law, F = k * |q1*q2| / r^2, where k is Coulomb's constant. For equilibrium, the magnitudes of F31 and F32 must be equal but in opposite directions since they are the only forces acting on q3.
Given that q1 = +2.00, q3 = +1.00, and the positions are y1=0, y2=6.00m, and y3=8.00m, we can write F31 = F32. Substituting the values and distances into Coulomb's formula, and solving for q2, we find that q2 must be -4.00 to achieve equilibrium. Hence, the correct answer is c. -4.00.
