Given:
Charge on first sphere, q1 = 7μC
Charge on second sphere, q2 = -5μC
Additional charge given to each sphere, Δq = -2μC

To find:
New force acting on each charge

Concepts used:
Coulomb's law, superposition principle

Solution:

Step 1: Find the original force F

The force between two charged spheres is given by Coulomb's law as:
F = k * |q1| * |q2| / r^2
where k is Coulomb's constant (9x10^9 Nm^2/C^2), r is the distance between the spheres, and |q1| and |q2| are the magnitudes of the charges.

Here, the charges are of opposite signs, so the force is attractive. Taking their magnitudes, we get:
F = k * 7μC * 5μC / r^2
F = 31.5 N / r^2 (approx.)

Step 2: Find the new force after adding -2μC to each sphere

When each sphere is given an additional charge of -2μC, the new charges become:
q1' = q1 - 2μC = 5μC
q2' = q2 - 2μC = -7μC

The new force between them is given by Coulomb's law as before, but with the new charges:
F' = k * |q1'| * |q2'| / r^2
F' = k * 5μC * 7μC / r^2
F' = 31.5 N / r^2 (approx.)

So the new force is also 31.5 N / r^2 (approx.), which means that adding the same amount of charge to each sphere did not change the force between them. This is because the charges are still of opposite signs and the distance between them did not change.

Conclusion:

The new force acting on each charge is 31.5 N / r^2 (approx.), which is the same as the original force. This can be explained by the superposition principle, which states that the total force on a charge due to several other charges is the vector sum of the forces due to each individual charge. Since the additional charges on each sphere are equal and opposite, they do not contribute any net force on the other sphere.