Seven charges are placed in the configuration as shown in the figure below, where the charges are
placed on the corners of a regular hexagon and its center. They all have a charge magnitude of Q=
4.15 µC. If the five charges (Solid Black) are positively charged and two negatively charged (White).
Note: The length of one side of the hexagon is 5.00x101
cm.
a) Find the net acting, Fnet on charge q7.
b) If charge q7 is removed from the center,
b.i. Calculate the net electric field, Enet at that center.
b.ii. Calculate the electric potential Vtotal at that center
Unfortunately, the figure you mentioned is missing in your question. Could you please provide the figure or describe the positions of the charges in more detail so that I can help you with the calculations?
a) To find the net acting force on charge q7, we need to calculate the individual forces between q7 and each of the other charges.
Let's call the positively charged charges (solid black) as q1, q2, q3, q4, and q5 and the negatively charged charges (white) as q6 and q7.
The force between two charges can be calculated using Coulomb's Law: F = k * (|q1| * |q2|) / r^2, where F is the force, k is the electrostatic constant, |q1| and |q2| are the magnitudes of the charges, and r is the distance between the charges.
Since the length of one side of the hexagon is given as 5.00x10^1 cm, we can calculate the distance between q7 and the other charges.
The distance between q7 and q1, q2, q3, q4, and q5 is equal to the length of one side of the hexagon, so it is 5.00x10^1 cm.
The distance between q7 and q6 is 2 times the distance between q7 and any of the other charges, so it is 2 * 5.00x10^1 cm = 1.00x10^2 cm.
The electrostatic constant is given by k = 8.99x10^9 N m^2/C^2.
Now we can calculate the individual forces:
The force between q7 and q1 is F1 = k * (|q7| * |q1|) / r^2 = 8.99x10^9 N m^2/C^2 * (4.15x10^-6 C * 4.15x10^-6 C) / (5.00x10^-1 m)^2.
Similarly, the forces between q7 and q2, q3, q4, q5 are F2, F3, F4, and F5, respectively.
The force between q7 and q6 is F6 = k * (|q7| * |q6|) / r^2 = 8.99x10^9 N m^2/C^2 * (4.15x10^-6 C * -4.15x10^-6 C) / (1.00x10^2 m)^2.
Finally, we can find the net acting force on charge q7 by summing up all these forces:
Fnet = F1 + F2 + F3 + F4 + F5 + F6.
b) If charge q7 is removed from the center:
b.i. The net electric field, Enet, at that center can be calculated using the formula Enet = Fnet / q7, where Fnet is the net acting force on charge q7 and q7 is the charge at the center.
b.ii. The electric potential, Vtotal, at that center can be calculated using the formula Vtotal = k * ∑(qi / ri), where qi is the charge of each of the other charges and ri is the distance between the center and each of the other charges.