Two identical objects have charges 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 touched together, then moved to a distance of separation of 2d, what will be the new force between them.
Ans: I tried the inverse square law and the coulomb`s law but i do not get the answer.
To find the new force between the two charged objects when they are moved to a distance of separation of 2d, we can use Coulomb's Law.
Coulomb's Law states that the force of attraction or repulsion between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between their centers.
Mathematically, the formula for Coulomb's Law is given as:
F = (k * |q1 * q2|) / r^2
Where:
F is the force between the two charges,
k is the electrostatic constant (k = 9.0 * 10^9 N m^2/C^2),
q1 and q2 are the charges of the objects,
and r is the distance between the centers of the objects.
In the given scenario, we have two identical objects with charges 6.0 * 10^-6 C and -2.0 * 10^-6 C respectively. When placed at a distance of d apart, their force of attraction is 2.0 N.
Using Coulomb's Law, we can substitute the given values into the formula:
2.0 N = (9.0 * 10^9 N m^2/C^2) * |6.0 * 10^-6 C * -2.0 * 10^-6 C| / (d)^2
Simplifying this equation, we get:
2.0 N = (9.0 * 10^9 N m^2/C^2) * 12.0 * 10^-12 C^2 / (d)^2
2.0 N = 108.0 N m^2/(d)^2
Now, let's find the new force when the distance of separation between the objects becomes 2d.
Using the same formula, we substitute the values:
F' = (k * |q1 * q2|) / (2d)^2
= (k * |q1 * q2|) / 4d^2
Now, we can compare the magnitudes of the forces:
|F'| / |F| = [(k * |q1 * q2|) / 4d^2] / [(k * |q1 * q2|) / d^2]
= (k * |q1 * q2|) / 4d^2 * (d^2) / (k * |q1 * q2|)
= 1/4
Therefore, the new force between the two charged objects, when they are moved to a distance of separation 2d, will be one-fourth (1/4) of the original force of attraction, which is 2.0 N.
Thus, the new force will be:
F' = 1/4 * F
= 1/4 * 2.0 N
= 0.5 N
To find the new force between the objects when they are moved to a distance of separation of 2d, we can use Coulomb's law. Coulomb's law states that the force between two charged objects is given by:
F = (k * |q1 * q2|) / r^2
Where:
F is the force between the objects,
k is the electrostatic constant (k = 8.99 x 10^9 N·m^2/C^2),
q1 and q2 are the charges of the objects, and
r is the distance between the objects.
In this case, the original force of attraction between the objects is 2.0N. Let's denote this as F1.
F1 = (k * |q1 * q2|) / d^2
To find the new force between the objects when they are moved to a distance of separation of 2d, let's denote it as F2.
F2 = (k * |q1 * q2|) / (2d)^2
Simplifying the equation:
F2 = (k * |q1 * q2|) / 4d^2
Now, let's substitute the given values into the equation and calculate the new force.
q1 = 6.0 x 10^-6 C
q2 = -2.0 x 10^-6 C
d = original distance
F1 = 2.0 N
F2 = (8.99 x 10^9 N·m^2/C^2 * |6.0 x 10^-6 C * -2.0 x 10^-6 C|) / (4 * d^2)
F2 = (8.99 x 10^9 N·m^2/C^2 * 12.0 x 10^-12 C^2) / (4 * d^2)
F2 = (107.88 x 10^-3 N·m^2/C^2) / (4 * d^2)
F2 = 26.97 x 10^-3 N·m^2/C^2 / d^2
Therefore, the new force between the objects when they are moved to a distance of separation of 2d is 26.97 x 10^-3 N·m^2/C^2 divided by d^2.