Four charges are placed at the four corners of a square of side 15 cm. The charges on the upper left and right corners are +3 μC and -6 μC respectively. The charges on the lower left and right corners are -2.4 μC and -9 μC respectively. The net electric force on -9 μC charge is:

a. 5.1 x1011 N/C away from the proton
b. 5.1 x1011 N/C toward the proton
c. 5.1 x1010 N/C toward the proton
d. 5.1 x1010 N/C away from the proton

To find the net electric force on the -9 μC charge, we need to calculate the electric forces between this charge and each of the other charges.

The formula to calculate the electric force between two charges is given by Coulomb's Law:

F = k * (|q1| * |q2|) / r^2

Where:
F is the magnitude of the electric force between the charges
k is the electrostatic constant (9 x 10^9 N m^2 / C^2)
|q1| and |q2| are the magnitudes of the charges
r is the distance between the charges

Let's calculate the electric forces:

1. For the upper left corner charge (+3 μC):
F1 = k * (|q1| * |q2|) / r^2
= (9 x 10^9 N m^2 / C^2) * (3 x 10^-6 C) * (9 x 10^-6 C) / (15 cm)^2
= (9 x 3 x 9) / (15^2) * 10^3 N
= 243 / 22500 * 10^3 N
= 10.8 N

2. For the upper right corner charge (-6 μC):
F2 = k * (|q1| * |q2|) / r^2
= (9 x 10^9 N m^2 / C^2) * (3 x 10^-6 C) * (6 x 10^-6 C) / (15 cm)^2
= (9 x 3 x 6) / (15^2) * 10^3 N
= 162 / 22500 * 10^3 N
= 7.2 N

3. For the lower left corner charge (-2.4 μC):
F3 = k * (|q1| * |q2|) / r^2
= (9 x 10^9 N m^2 / C^2) * (3 x 10^-6 C) * (2.4 x 10^-6 C) / (15 cm)^2
= (9 x 3 x 2.4) / (15^2) * 10^3 N
= 64.8 / 22500 * 10^3 N
= 2.88 N

4. For the lower right corner charge (-9 μC):
F4 = k * (|q1| * |q2|) / r^2
= (9 x 10^9 N m^2 / C^2) * (3 x 10^-6 C) * (9 x 10^-6 C) / (15 cm)^2
= (9 x 3 x 9) / (15^2) * 10^3 N
= 243 / 22500 * 10^3 N
= 10.8 N

Since the charges are placed at the four corners of a square, the electric forces in the x and y directions will cancel out. We are only concerned with the net force in the vertical direction (y-direction).

The charges (+3 μC and -6 μC) at the top corners will produce a downward force, while the charges (-2.4 μC and -9 μC) at the bottom corners will produce an upward force.

Net Force (F_net) = (F2 + F4) - (F1 + F3)
= (7.2 N + 10.8 N) - (10.8 N + 2.88 N)
= 18 N - 13.68 N
= 4.32 N

Since the net force is positive (upward), the answer is (c) 5.1 x 10^10 N/C toward the proton.