Two identical objects have charges from +6.0*10^-6 and -2.0*10^-6, respectively. When placed a distance d apart, their force of attraction is 2,0N. If the objects are touched together, then they moved to a distance of separation of 2d, what will be the new force between them?
Ans: I tried the finding the distance d and then finding the new force, but i am not getting the value, i even tried the inverse square law , i got the same answer but not the one required 0.17N.
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To find the new force between the objects when they are moved to a distance of separation of 2d, we need to consider the principle of superposition and the inverse square law for electric forces.
First, let's find the distance d between the two objects. We know that their force of attraction is 2.0 N. Using Coulomb's law, we can write:
F = k * |q1 * q2| / r^2,
where F is the force of attraction, k is Coulomb's constant (k = 9.0 * 10^9 Nm^2/C^2), q1 and q2 are the charges of the objects, and r is the distance between them.
Plugging in the values we have: q1 = +6.0 * 10^-6 C, q2 = -2.0 * 10^-6 C, and F = 2.0 N, we can solve the equation for r:
2.0 N = (9.0 * 10^9 Nm^2/C^2) * |(+6.0 * 10^-6 C) * (-2.0 * 10^-6 C)| / r^2.
Simplifying this equation, we get:
r^2 = [(9.0 * 10^9 Nm^2/C^2) * (6.0 * 10^-6 C) * (2.0 * 10^-6 C)] / 2.0 N.
r^2 = 108 m^2.
Taking the square root of both sides, we find:
r ≈ 10.39 m.
Now, when we touch the two objects together and move them to a distance of separation of 2d, the total charge becomes q = q1 + q2 = (+6.0 * 10^-6 C) + (-2.0 * 10^-6 C) = +4.0 * 10^-6 C.
Let's calculate the new force using the same equation and the new distance of separation 2d:
F' = (9.0 * 10^9 Nm^2/C^2) * |(+4.0 * 10^-6 C) * (+4.0 * 10^-6 C)| / (2d)^2.
F' = (9.0 * 10^9 Nm^2/C^2) * (16 * 10^-12 C^2) / (4 * d^2).
F' = (36 * 10^-3 Nm^2/C^2) / d^2.
Now, we can substitute d = 2.0 * 10.39 m into the equation for F':
F' = (36 * 10^-3 Nm^2/C^2) / (2.0 * 10.39 m)^2.
F' ≈ 0.17 N.
Therefore, the new force between the objects when they are moved to a distance of separation of 2d is approximately 0.17 N.