Two small, identical metal spheres contain excess charges of -10.0 x 10^-6 C and 6.0 x 10^-6 C, respectively. The spheres are mounted on insulated stands and placed 0.40 m apart. Determine the magnitude and direction of the force between the spheres.
F =k•q1•q2/r²,
where
k =9•10^9 N•m²/C²,
q1 =10•10^-6 C (!!! - with "plus" as we use the magnitude of the charge),
q2 = 6•10^-6 C,
r = 0.4 m.
The charges are of the opposite signs => they are attracting.
To determine the magnitude and direction of the force between the spheres, we can use Coulomb's Law.
Coulomb's Law states that the magnitude of the electric force between two charged objects is directly proportional to the product of the magnitudes of their charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is:
F = k * q1 * q2 / r^2
Where:
F is the magnitude of the force between the spheres,
k is the electrostatic constant (a constant value),
q1 and q2 are the charges on the spheres, and
r is the distance between the spheres.
Now, let's plug in the given values:
q1 = -10.0 x 10^-6 C (charge of the first sphere)
q2 = 6.0 x 10^-6 C (charge of the second sphere)
r = 0.40 m (distance between the spheres)
Note: The electrostatic constant k is typically expressed as 9 x 10^9 Nm^2/C^2.
Using these values, let's calculate the magnitude of the force between the spheres.
F = (9 x 10^9 Nm^2/C^2) * (-10.0 x 10^-6 C) * (6.0 x 10^-6 C) / (0.40 m)^2
To solve, perform the multiplication and division:
F = (9 x 10^9 Nm^2/C^2) * (-10.0 x 10^-6 C) * (6.0 x 10^-6 C) / (0.40 m)^2
F = -1.35 x 10^-2 N
Therefore, the magnitude of the force between the spheres is 1.35 x 10^-2 N.
To determine the direction of the force, we need to consider the charges on the spheres. Since one sphere is negatively charged and the other is positively charged, they will attract each other. Therefore, the force between the spheres is directed towards each other.
In conclusion, the magnitude of the force between the spheres is 1.35 x 10^-2 N, and the direction of the force is towards each other.