Question

Two small objects each with a net charge of +Q exert a force of magnitude F on each other. We replace one of the objects with another whose net charge is + 4Q. We move the +Q and +4Q charges to be 3 times as far apart as they were. What is the magnitude of the force on the +4Q charge ?

A. F

B. 4F

C. 4F/3

D. 4F/9

E. F/3

Answer 1

The magnitude of the force on the +4Q charge, after replacing one of the original +Q charges and moving the charges three times farther apart, is calculated to be 4F/9 using Coulomb's Law. Therefore, the correct answer is D.

Step-by-step explanation:

The magnitude of the electrostatic force between two charges can be described by Coulomb's Law, which states that F = k × (q1 × q2) / r^2, where F is the force between the charges, k is Coulomb's constant, q1 and q2 are the magnitudes of the charges, and r is the distance between the centers of the two charges. Originally, two objects each with charge +Q exert a force of magnitude F on each other. After one charge is replaced with a +4Q charge and they are moved to be three times as far apart, the force on the +4Q charge can be calculated using the modified version of Coulomb's Law that takes into account the new charges and distance.

Using the original scenario as a reference, where F = k × (Q × Q) / r^2, when the charge is replaced and the distance is tripled, the new force F' = k × (Q × 4Q) / (3r)^2 = 4kQ^2 / 9r^2. By comparing F' with F, we find that F' = (4/9)F. Thus, the magnitude of the force on the +4Q charge is 4F/9.

Answer 2

F'= 4F/9

Step-by-step explanation:

Two small objects each with a net charge of +Q exert a force of magnitude F on each other. If r is the distance between them, then the force is given by :

`F=(kQ^2)/(r^2)` ...(1)

Now, if one of the objects with another whose net charge is + 4Q is replaced and also the distance between +Q and +4Q charges is increased 3 times as far apart as they were. New force is given by :

`F'=(kQ* 4Q)/((3r)^2)\\\\F'=(4kQ^2)/(9r^2)`.....(2)

Dividing equation (1) and (2), we get :

`(F)/(F')=((kQ^2)/(r^2))/((4kQ^2)/(9r^2))\\\\(F)/(F')=(kQ^2)/(r^2)* (9r^2)/(4kQ^2)\\\\(F)/(F')=(9)/(4)\\\\F'=(4F)/(9)`

Hence, the correct option is (d) i.e. " 4F/9"