Two spheres 4cm apart, attract each other with a force of 1.2×10^9N. Determine the magnitude of the charge on each tosee if one has two the charge (of the opposite sign) as the other?

To determine the magnitude of the charge on each sphere, we can use Coulomb's Law:

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

Where:
F = force between the spheres (1.2×10^9N)
k = Coulomb's constant (8.99 x 10^9 N m^2/C^2)
q1 and q2 = charges on the spheres
r = distance between the spheres (4cm = 0.04m)

Plugging in the values:

1.2×10^9N = (8.99 x 10^9 N m^2/C^2) * (q1 * q2) / (0.04m)^2

1.2×10^9N = (8.99 x 10^9 N m^2/C^2) * (q1 * q2) / 0.0016m^2

1.2×10^9N = 5.61875 x 10^12 * q1 * q2

q1 * q2 = 1.2×10^9N / 5.61875 x 10^12

q1 * q2 = 0.2134 x 10^-3

Since we are looking for the magnitude of the charge on each sphere, we can assume that one charge is positive and the other is negative. Therefore, we can write:

q1 = q
q2 = -q

Substitute these values into the equation:

q * -q = 0.2134 x 10^-3

-q^2 = 0.2134 x 10^-3

q^2 = -0.2134 x 10^-3

q = sqrt(-0.2134 x 10^-3)

q = 0.462 C

Therefore, the magnitude of the charge on each sphere is 0.462 C. This means that one sphere has twice the charge (of the opposite sign) as the other.