Two charged particles exert an electrostatic force of 27 N on each other. What will the magnitude of the force be if the distance between the two charges is increased to three times the original distance?
Isn't force inversely proportional to the square of distance?
forcenew=force old /9 ?
To determine the magnitude of the force when the distance between the two charges is increased to three times the original distance, we can use Coulomb's law. Coulomb's law states that the electrostatic force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Let's denote the original distance between the charges as "d" and the magnitude of the force as "F".
According to Coulomb's law, the force is given by the equation:
F = k * (q1 * q2) / d^2
Where:
F is the magnitude of the electrostatic force
k is the electrostatic constant (approximately 9 x 10^9 Nm^2/C^2)
q1 and q2 are the charges of the two particles
d is the distance between the charges
In our case, we are given that the force is 27 N. Let's say the charges of the two particles are q1 and q2.
F = 27 N
k = 9 x 10^9 Nm^2/C^2
Now, if the distance between the charges is increased to three times the original distance, then the new distance would be 3d.
Using Coulomb's law, we can set up the equation for the new force, F_new, based on the new distance:
F_new = k * (q1 * q2) / (3d)^2
Simplifying this equation, we have:
F_new = k * (q1 * q2) / (9 * d^2)
We need to find the magnitude of the new force, F_new. To do this, we can use the fact that the magnitude of the force is directly proportional to the charges and inversely proportional to the square of the distance.
Since the product of the charges remains the same, q1 * q2, the magnitude of the new force, F_new, will be 1/9 times the original force, F.
Thus, the magnitude of the force when the distance between the two charges is increased to three times the original distance will be 1/9 * 27 N = 3 N.
To determine the magnitude of the force between the two charged particles when the distance between them is increased, we can use Coulomb's Law.
Coulomb's Law states that the electrostatic force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Mathematically, Coulomb's Law is given by:
F = k * (q1 * q2) / r^2
Where:
F is the magnitude of the electrostatic force between the charges,
k is the electrostatic constant (k = 9 x 10^9 Nm^2/C^2),
q1 and q2 are the charges of the particles, and
r is the distance between the charges.
In this case, we are given that the initial force between the charges is 27 N. Let's assume that the initial distance between the charges is represented by r1.
We also know that the distance is increased to three times the original distance. Thus, the new distance between the charges can be represented as 3r1.
To find the new magnitude of the force, let's call it F', we need to substitute the new values into Coulomb's Law:
F' = k * (q1 * q2) / (3r1)^2
Now, we can calculate the magnitude of the force when the distance between the two charges is increased to three times the original distance by substituting the appropriate values.