Two identical point charges are separated by a distance of 3.0 cm and they repel each other with a force of 4 X 10^-5 N. What is the new force if the distance between the point charges is doubled?
An inverse square law applies tp both gravitational and electrostatic forces.
If you double the distance between two objects, the force is decreased by a factor of 1/2^2, which is 1/4
Multiply that by the original force and you get 1 x 10^-5 N
Well, if the distance between the point charges is doubled, they'll have more space to avoid each other's personal space, so they'll repel each other less. It's like when you double the distance between two people having a tickle fight, it's just not as intense anymore.
To figure out the new force, we can use the inverse square law for electric force, which states that the force between two point charges is inversely proportional to the square of the distance between them.
So, if the distance between the charges is doubled, we can multiply the original force by the inverse square of 2 (which is 1/2^2 = 1/4) to find the new force.
The original force is 4 x 10^-5 N, so when we multiply it by 1/4, we get a new force of 1 x 10^-5 N.
Therefore, the new force between the point charges, when the distance is doubled, is 1 x 10^-5 N.
To find the new force when the distance between the point charges is doubled, we can use Coulomb's law, which states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. The formula is given by:
F = k * (q1 * q2) / r^2,
where F is the force, k is the electrostatic constant, q1 and q2 are the charges of the point charges, and r is the distance between them.
Given that the original force is 4 x 10^-5 N and the initial distance is 3.0 cm (which is 0.03 m), we can substitute these values into the equation to find k.
4 x 10^-5 N = k * (q1 * q2) / (0.03 m)^2.
Now, let's consider when the distance between the point charges is doubled. The new distance will be 2 times the initial distance, or 2 * 0.03 m = 0.06 m.
Now, we can rearrange the equation to find the new force:
F_new = k * (q1 * q2) / (0.06 m)^2.
To find the new force, we need to calculate k. The value of k is the electrostatic constant, which is approximately 9 x 10^9 N⋅m^2/C^2.
Substituting the known values into the equation:
4 x 10^-5 N = (9 x 10^9 N⋅m^2/C^2) * (q1 * q2) / (0.03 m)^2.
Simplifying:
4 x 10^-5 N = (9 x 10^9 N⋅m^2/C^2) * (q1 * q2) / 0.0009 m^2.
Now, we can solve for (q1 * q2):
(q1 * q2) = (4 x 10^-5 N) * (0.0009 m^2) / (9 x 10^9 N⋅m^2/C^2).
Simplifying:
(q1 * q2) = 4 x 10^-5 C^2.
Now, we can substitute this value into the equation for the new force:
F_new = (9 x 10^9 N⋅m^2/C^2) * (4 x 10^-5 C^2) / (0.06 m)^2.
Simplifying:
F_new = (9 x 10^9 N⋅m^2/C^2) * 4 x 10^-5 C^2 / (0.06 m)^2.
Calculating:
F_new ≈ 2.25 x 10^-5 N.
Therefore, the new force when the distance between the point charges is doubled is approximately 2.25 x 10^-5 N.
To calculate the new force between two point charges when the distance between them is doubled, we need to apply Coulomb's Law. Coulomb's Law states that the force between two point charges 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) / r^2
Where:
F is the force between the charges,
k is the Coulomb's constant (approximately 9 x 10^9 N m^2/C^2),
q1 and q2 are the magnitudes of the charges, and
r is the distance between the charges.
In this case, we know the initial force (4 x 10^-5 N) and the initial distance (3.0 cm = 0.03 m). Let's call the charges q1 and q2, and the initial force F1.
F1 = (k * q1 * q2) / (0.03)^2
Now, let's calculate the new force when the distance is doubled. The new distance would be 2 times the initial distance (r_new = 2 * 0.03 m = 0.06 m). Let's call the new force F2.
F2 = (k * q1 * q2) / (0.06)^2
To find the ratio between the new force (F2) and the initial force (F1), we can divide the two equations:
(F2 / F1) = [(k * q1 * q2) / (0.06)^2] / [(k * q1 * q2) / (0.03)^2]
By canceling out the common terms:
(F2 / F1) = (0.03)^2 / (0.06)^2
Now, let's calculate this ratio:
(F2 / F1) = (0.03)^2 / (0.06)^2 = 1/4
Therefore, the new force (F2) is one-fourth (1/4) of the initial force (F1).
F2 = (1/4) * F1 = (1/4) * 4 x 10^-5 N = 1 x 10^-5 N
Hence, the new force when the distance between the point charges is doubled would be 1 x 10^-5 N.