Two charges separated by 1 meter exert a 1 N force on eachother. If the magnitude of each charge is doubled, the force on each charge is?

Question

Two charges separated by 1 meter exert a 1 N force on eachother. If the magnitude of each charge is doubled, the force on each charge is?

Answer 1

F = k Q1 Q2/r^2

Q1' = 2 Q1
Q2' = 2 Q2
so
4 times

Answer 2

Is not my question?

Answer 3

The force between two charges is given by Coulomb's Law:

F = (k * q1 * q2) / r^2

where F is the force, k is the electrostatic constant (9 * 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, the charges are separated by 1 meter and exert a force of 1 N on each other. Let's call the magnitude of each charge q.

So the given equation becomes:

1 N = (k * q * q) / (1 m)^2

Simplifying, we get:

1 N = (k * q^2) / 1 m^2

Since k is a constant, we can rearrange the equation to solve for q^2:

q^2 = (1 N * 1 m^2) / k

Now, if we double the magnitude of each charge, the new charge magnitude would be 2q. Let's call the force between the charges with the new magnitudes F'.

The new equation becomes:

F' = (k * (2q) * (2q)) / (1 m)^2

Simplifying, we get:

F' = 4 * ((k * q^2) / (1 m)^2)

We know that the original force was 1 N, so the new force F' would be:

F' = 4 * (1 N) = 4 N

Therefore, if the magnitude of each charge is doubled, the force on each charge would be 4 N.

Answer 4

To determine the force on each charge when the magnitude of each charge is doubled, we can use Coulomb's law. Coulomb's law states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Mathematically, Coulomb's law can be written as:

F = k * (q1 * q2) / r^2

Where:
F is the force between the charges,
k is Coulomb's constant (approximately equal to 9 × 10^9 N⋅m^2/C^2),
q1 and q2 are the magnitudes of the charges, and
r is the distance between the charges.

Given that the charges are separated by 1 meter and exert a 1 N force on each other, we can rearrange Coulomb's law to solve for the magnitudes of the charges.

1 = k * (q1 * q2) / 1^2

Since the distance is 1 meter, we can simplify the equation to:

1 = k * (q1 * q2)

Now, if we double the magnitude of each charge, the new magnitudes would be 2q1 and 2q2. Plugging these values into the equation, we get:

1 = k * (2q1 * 2q2)

Now we can compare the old and new forces by dividing the two equations:

(1 N) / 1 = (k * (q1 * q2)) / (k * (2q1 * 2q2))

Simplifying:

1 = (q1 * q2) / (4q1 * 4q2)

1 = 1 / (4 * 4)

1 = 1 / 16

Therefore, when the magnitude of each charge is doubled, the force on each charge is 1/16 N or 0.0625 N.