Two insulating spheres with charges of -7.0 μC and -12 μC, are located 10.0 cm apart.
What is the force between them?
In what direction does it act?
like sign charges repel each other
10 cm = 0.10 meter
k = 9*10^9
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To calculate the force between two charged objects, we can use Coulomb's Law, which 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 force between the objects
k is Coulomb's constant ≈ 9.0 x 10^9 N m^2/C^2
q1 and q2 are the charges of the objects
r is the distance between the centers of the objects
Given:
q1 = -7.0 μC (microcoulomb)
q2 = -12 μC (microcoulomb)
r = 10.0 cm = 0.10 m (converted to meters)
Now, let's plug in these values into the formula to calculate the force:
F = (k * |q1 * q2|) / r^2
= (9.0 x 10^9 N m^2/C^2 * |-7.0 μC * -12 μC|) / (0.10 m)^2
To simplify the calculation, we need to convert the charges into coulombs:
-7.0 μC = -7.0 x 10^-6 C
-12 μC = -12 x 10^-6 C
Substituting these values:
F = (9.0 x 10^9 N m^2/C^2 * |-7.0 x 10^-6 C * -12 x 10^-6 C|) / (0.10 m)^2
Now, calculate the force using a calculator. The magnitude and direction of the force will be determined by the calculated value.
After performing the calculation, the force between the two charged spheres is found to be approximately 3.36 x 10^-2 N (Newtons).
Since both charges are negative, the force acts in the direction away from each other, that is, repulsive.