Two objects separated by a distance r are each carrying a charge –q. The magnitude of the force exerted on the second object by the first is F. If the first object is removed and replaced with an identical object that carries a charge +4q, what is the magnitude of the electric force on the second object?

-4 F (opposite charges attract)

4f

4F

To find the magnitude of the electric force on the second object after replacing the first object, we need to use Coulomb's law. Coulomb's law states that the electric 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.

Let's break down the steps to find the magnitude of the electric force on the second object:

Step 1: Calculate the electric force between the two objects with charge -q using Coulomb's law.
The formula for Coulomb's law is:
F = (k * |q1 * q2|) / r^2

where:
- F is the magnitude of the electric force
- k is the electrostatic constant (k = 9 × 10^9 N * m^2 / C^2)
- q1 and q2 are the charges of the two objects
- r is the distance between the two objects

In this case, q1 = -q, q2 = -q, and we denote the resulting force as F.

Step 2: Substitute the new charge (+4q) into the formula and calculate the new magnitude of the electric force.
q1 = +4q, q2 = -q, and the distance remains the same (r).

Using Coulomb's law:
F' = (k * |q1 * q2|) / r^2

Step 3: Determine the ratio between the new magnitude of the electric force (F') and the original magnitude of the electric force (F).
F' / F = (k * |q1' * q2|) / r^2 / (k * |q1 * q2|) / r^2

Step 4: Simplify the expression by canceling out terms and evaluating the ratio.
F' / F = (|q1'| / |q1|)

Substituting the values:
F' / F = (|+4q| / |-q|)

Step 5: Calculate the ratio F' / F.
Since q is a scalar value (positive or negative doesn't affect its magnitude), we have:
|+4q| / |-q| = 4

Therefore, the magnitude of the electric force on the second object after replacing the first object will be 4 times the original magnitude of the electric force.