Seven charges are placed in the configuration, 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.(7 marks)
b) If charge q7 is removed from the center,
b.i. Calculate the net electric field, Enet at that center. (7 marks)
b.ii.Calculate the electric potential Vtotal at that center. (8 marks)
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To find the net acting force (Fnet) on charge q7, we need to consider the forces between q7 and each of the other charges.
a) Fnet on charge q7:
The force between two charges can be found using Coulomb's Law, which states that the force (F) between two charges (q1 and q2) is given by:
F = (k * |q1| * |q2|) / r^2
Where k is the Coulomb's constant (k ≈ 8.99 x 10^9 N m^2/C^2), |q1| and |q2| are the magnitudes of the charges, and r is the distance between them.
In the given configuration, we have five positively charged charges (Solid Black) and two negatively charged charges (White). Let's label them as q1, q2, q3, q4, q5, q6, and q7. We will also assume q1 to q5 are the positively charged charges, and q6 and q7 are the negatively charged charges.
The charges:
q1 = q2 = q3 = q4 = q5 = 4.15 µC (Positive charges)
q6 = q7 = -4.15 µC (Negative charges)
The distance between each charge and q7 is the length of one side of the hexagon, which is 5.00 x 10^1 cm = 500 cm = 5.00 m (converting to SI units).
Now, let's calculate the force between q7 and each of the other charges:
1. Force between q7 and q1:
F1 = (k * |q7| * |q1|) / r^2
Substituting the values, we get:
F1 = (8.99 x 10^9 N m^2/C^2) * (4.15 x 10^(-6) C) * (4.15 x 10^(-6) C) / (5.00 m)^2
2. Similarly, calculate the forces between q7 and q2, q3, q4, q5, q6.
To find the net acting force Fnet on q7, we need to sum up all the forces acting on it:
Fnet = F1 + F2 + F3 + F4 + F5 + F6
Now, plug in the values you get from the calculations above and sum them up to find the net acting force on charge q7.
b) If charge q7 is removed from the center:
b.i. To find the net electric field (Enet) at the center, we need to calculate the electric fields produced by each of the charges at that point and then sum them up.
The electric field (E) produced by a point charge q at a distance r from it is given by:
E = k * |q| / r^2
Using Coulomb's constant k ≈ 8.99 x 10^9 N m^2/C^2, we can calculate the electric field produced by each charge and sum them up to find the net electric field at the center.
b.ii. To calculate the electric potential (Vtotal) at the center, we can use the equation:
V = k * q / r
Where V is the electric potential, q is the charge, r is the distance from the charge.
Similar to the previous step, calculate the electric potential produced by each charge and sum them up to find the total electric potential at the center.