If two small non-conducting spheres separated by a distance of 6 centimeters carry charges of q1 = +2 µC and q2 = +4 mC. What will be the net electric force between the two spheres? Sketch and show the directions of the electric forces.
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To find the net electric force between the two spheres, we can use Coulomb's Law:
F = k * |q1 * q2| / r^2
where F is the electric force, k is the electrostatic constant (9 x 10^9 N*m^2/C^2), q1 and q2 are the charges on the spheres, and r is the distance between the centers of the spheres.
Given:
q1 = +2 µC = 2 x 10^-6 C
q2 = +4 mC = 4 x 10^-3 C
r = 6 cm = 6 x 10^-2 m
Plugging in the values:
F = (9 x 10^9 N*m^2/C^2) * |(2 x 10^-6 C) * (4 x 10^-3 C)| / (6 x 10^-2 m)^2
Simplifying:
F = (9 x 10^9 N*m^2/C^2) * (8 x 10^-9 C^2) / (36 x 10^-4 m^2)
F = 2 N
The net electric force between the two spheres is 2 N.
To sketch and show the directions of the electric forces, we can assume that the force between the spheres is attractive (since the charges have opposite signs). This means that Sphere 1 (with charge q1) will experience an electric force towards Sphere 2 (with charge q2). Similarly, Sphere 2 will experience an electric force towards Sphere 1.
Hence, the sketch would show two arrows pointing towards each other from the center of each sphere to represent the direction of the electric forces.
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