Final answer:
a) The x-component of the electric field at point A is 1.10 × 10^5 N/C, and the y-component is 0.300 N/C.
b) To nullify the total electric field at point A, an additional charge q₃ of -6.91 nC needs to be placed at point B.
Step-by-step explanation:
a) To calculate the electric field components at point A, we consider the contributions from the two charges. For the x-component, due to symmetry, the contributions cancel each other, resulting in an electric field of 0 in the x-direction. For the y-component, the electric field due to q₁ and q₂ are in the same direction. Using Coulomb's law, E = k * |q| / r², where k is Coulomb's constant, q is the charge, and r is the distance from the charge to the point of interest, we calculate the electric field due to q₁ and q₂, then add them together to find the total y-component at point A.
b) To determine the additional charge q₃ needed at point B to nullify the total electric field at point A, we consider the contributions from all charges. Since the x-component at A is already zero, we aim to cancel the y-component. Given the distances and charges involved, we set up the equation to find the charge q₃ at point B. This equation considers the distances and signs of charges to ensure the net electric field at A is zero.
By summing the contributions of the charges using Coulomb's law and solving the equation, we find that a charge of -6.91 nC placed at point B would produce an electric field that nullifies the total electric field at point A. This is necessary due to the combined effects of q₁, q₂, and the additional charge q₃.
Complete Question:
Part A Constants Calculate the electric field at point A, located at coordinates (0 m, 12.0 m Two point charges are placed on the x axis. (Figure 1)The first charge, q1-8.00 nC , is placed a distance 16.0 m from the origin along the positive x axis; the second charge, 26.00 nC, is placed a distance 9.00 m from the origin along the negative x axis. Give the x and y components of the electric field as an ordered pair. Express your answer in newtons per coulomb to three significant figures. View Available Hint(s) A, EAy 0,0.300 N/C Correct Term 1: Significant Figures Feedback: Your answer 1.10-51x10-5 N/C was either rounded differently or used a different number of significant figures than required for this part. ▼ Part B An unknown additional charge qs is now placed at point B, located at coordinates (0 m, 15.0 m). Find the magnitude and sign of g3 needed to make the total electric field at point A equal to zero. Figure 1 of 1 Express your answer in nanocoulombs to three significant figures. View Available Hint(s) B (Om. 15 m) A (0 m, 12 m) 0回 nC 0(0111. 0 m) 92 -9 m, 0m) q1 16 m, 0 m)