Question

The distance between two particles is 2 centimeters. If the distance is increased to 4 centimeters, the force will be ?

Answer 1

The new force is 1/4 of the previous force.

Step-by-step explanation:

Given

`Initial\ Distance = 2cm` ----
`r_1`

`New\ Distance = 4cm` ---
`r_2`

Required

Determine the new force

Let the two particles be q1 and q2.

The initial force F1 is:

`F_1 = (kq_1q_2)/(r_1^2)` --- Coulomb's law

Substitute 2 for r1

`F_1 = (kq_1q_2)/(2^2)`

`F_1 = (kq_1q_2)/(4)`

The new force (F2) is

`F_2 = (kq_1q_2)/(r_2^2)`

Substitute 4 for r2

`F_2 = (kq_1q_2)/(4^2)`

`F_2 = (kq_1q_2)/(4*4)`

`F_2 = (1)/(4)*(kq_1q_2)/(4)`

Substitute
`F_1 = (kq_1q_2)/(4)`

`F_2 = (1)/(4)*F_1`

`F_2 = (F_1)/(4)`

The new force is 1/4 of the previous force.