A metal sphere with a charge of +25 x 10-9 C is placed 2 m away from another metal sphere which carries a charge of +10 x 10^-9 C. What is the magnitude and direction of the electric force between the two metal spheres?
To find the magnitude and direction of the electric force between the two metal spheres, we can use Coulomb's Law. Coulomb's Law states that the force between two charged objects is directly proportional to the product 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 electric force
k is the electrostatic constant (k = 9 x 10^9 Nm^2/C^2)
q1 and q2 are the charges of the two spheres
r is the distance between the centers of the two spheres
Given:
q1 = +25 x 10^-9 C (charge of the first sphere)
q2 = +10 x 10^-9 C (charge of the second sphere)
r = 2 m (distance between the spheres)
Now, let's substitute these values into the formula and solve for the magnitude of the electric force:
F = (9 x 10^9 Nm^2/C^2) * (|25 x 10^-9 C| * |10 x 10^-9 C|) / (2 m)^2
Simplifying the expression:
F = (9 x 10^9 Nm^2/C^2) * (25 x 10^-9 C) * (10 x 10^-9 C) / 4 m^2
F = (9 x 25 x 10^-9 C^2 x 10^-9 C) / 4 x 10^9 m^2
F = 225 x 10^-18 N / 4 x 10^9 m^2
F = 56.25 x 10^-27 N / 10^9 m^2
F = 5.625 x 10^-18 N / m^2
Therefore, the magnitude of the electric force between the two metal spheres is approximately 5.625 x 10^-18 N/m^2.
To find the direction of the electric force, we can use the principle that like charges repel each other. Since both spheres have positive charges, they will repel each other. Thus, the direction of the electric force is away from each other along the line connecting their centers.