There are two charged particles. They exert an electrostatic force of 10 N on each other. Suppose the distance between the two particles is increased to five times the original distance. What will the magnitude of the force?
To answer this question, we can use Coulomb's Law, which states that the magnitude of 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.
The formula for Coulomb's Law is:
F = k * (|q1| * |q2|) / d^2
Where:
F is the magnitude of the electrostatic force,
k is a constant called the electrostatic constant (k = 8.99 x 10^9 N m^2 / C^2),
q1 and q2 are the charges of the two particles, and
d is the distance between the particles.
In this case, we know that the original electrostatic force between the two particles is 10 N. Let's assume that their charges are q1 and q2, respectively. The initial distance between them is unknown, but we can represent it as d.
So, we have the equation:
10 = k * (|q1| * |q2|) / d^2
Now, if we increase the distance between the particles to five times the original distance (5d), we need to find the new magnitude of the electrostatic force.
The formula remains the same:
F = k * (|q1| * |q2|) / (5d)^2
To find the new force, we can substitute F with 10, and substitute d with 5d in the equation. This gives us:
10 = k * (|q1| * |q2|) / (5d)^2
Simplifying further:
10 = k * (|q1| * |q2|) / 25d^2
Multiplying both sides of the equation by 25d^2, we get:
250d^2 = k * (|q1| * |q2|)
From the equation, we can see that the magnitude of the force is directly proportional to the products of the charges (|q1| * |q2|), and it is independent of the distance between the particles.
Therefore, even if the distance is increased to five times the original distance, the magnitude of the force will remain the same, which is 10 N in this case.
The magnitude of the electrostatic force between two charged particles is given by Coulomb's law:
F = k * (q1 * q2) / r^2
Where:
F is the force between the charges,
k is Coulomb's constant (8.99 x 10^9 N m^2/C^2),
q1 and q2 are the magnitudes of the charges of the particles,
r is the separation distance between the particles.
In this case, since both particles exert a force of 10 N on each other, we can assume that the magnitudes of the charges (q1 and q2) are the same.
Let's denote the original distance between the particles as 'r0' and the new distance as '5r0'.
According to the inverse square relationship in Coulomb's law, if the distance between two charged particles is increased by a factor of 'n', the magnitude of the force will decrease by a factor of 'n^2'.
Therefore, the magnitude of the force when the distance is increased to five times the original distance is:
F_new = F * (r0 / 5r0)^2
= F * (1/25)
= 10 N * (1/25)
= 0.4 N
Hence, the magnitude of the force when the distance is increased to five times the original distance is 0.4 N.
since F = qq/r^2, changing r to 5r means you now have
qq/(5r)^2 = qq/25r^2 = 1/25 * qq/r^2 = 1/25 F