Two charges separated by a distance of 1 m exert a 1.0N force on each other. If the changes are pulled to a 3-m separation distance, the force on each charge will be
0.11 N
To find the force on each charge when they are pulled to a 3 m separation distance, we can use Coulomb's law, which states that the force between two charges is given by:
F = k * (q1 * q2) / r^2
Where:
F is the force between the charges,
k is Coulomb's constant (approximately equal to 9 x 10^9 N m^2/C^2),
q1 and q2 are the magnitudes of the charges, and
r is the separation distance between the charges.
Given that the force on each charge is 1.0 N when the separation distance is 1 m, we can set up the equation as follows:
1.0 N = (9 x 10^9 N m^2/C^2) * (q1 * q2) / (1 m)^2
We can now rearrange the equation to solve for (q1 * q2):
(q1 * q2) = (1.0 N * (1 m)^2) / (9 x 10^9 N m^2/C^2)
(q1 * q2) = 1.0 N * (1 m)^2 / 9 x 10^9 N m^2/C^2
(q1 * q2) = 1 / 9 x 10^9 C^2
Now, let's calculate the force on each charge when they are pulled to a 3 m separation distance. Using the same equation as before, but substituting the new separation distance, we get:
F_new = (9 x 10^9 N m^2/C^2) * (q1 * q2) / (3 m)^2
F_new = (9 x 10^9 N m^2/C^2) * (1 / 9 x 10^9 C^2) / (3 m)^2
F_new = (1/3) N
Therefore, the force on each charge when they are pulled to a 3 m separation distance is 1/3 N.
To find the force on each charge at a new separation distance, we can use Coulomb's Law, which states that the force between two charges is proportional to the product of their charges and inversely proportional to the square of the separation distance.
Coulomb's Law equation:
F = k * (q1 * q2) / r^2
where,
F = force between the charges
k = Coulomb's constant (k = 9 × 10^9 N m^2/C^2)
q1, q2 = charges
r = separation distance between the charges
Given:
F = 1.0 N (force on each charge)
r_initial = 1 m (initial separation distance)
Let's first calculate the product of the charges (q1 * q2) using the initial force and separation distance.
1.0 N = k * (q1 * q2) / (1 m)^2
Now, we need to find the new force at a separation distance of 3 m. Let's denote the new force as F_new.
F_new = k * (q1 * q2) / (3 m)^2
To find F_new, we need to know the value of (q1 * q2). Let's solve our first equation for (q1 * q2).
1.0 N = k * (q1 * q2) / (1 m)^2
q1 * q2 = (1.0 N * (1 m)^2) / k
Substituting this value in the equation for F_new:
F_new = k * [(1.0 N * (1 m)^2) / k] / (3 m)^2
Simplifying further:
F_new = (1.0 N * (1 m)^2) / (3 m)^2
Calculating the final value:
F_new = 1.0 N * (1/9) = 0.111 N
Therefore, if the charges are pulled to a 3 m separation distance, the force on each charge will be approximately 0.111 N.
F₁=k•q₁•q₂/r₁²,
F₂=k•q₁•q₂/r₂²,
F₁/F₂=k•q₁•q₂•r₂² / k•q₁•q₂•r₁²,
F₂= F₁• r₁²/r ₂².