Question

What will happen to the force if we
decrease r by a factor of 2 ?
​

Answer 1

The new force will become 1/4 times of the initial force.

Step-by-step explanation:

The Coulomb force between two charges is directly proportional to the product of charges and inversely proportional to the square of the distance between them.

It can be given by :

`F=k(q_1q_2)/(r^2)` ....(1)

r is distance

If we decrease the r by a factor of 2, r'=2r.

New force will become,

`F'=k(q_1q_2)/(r'^2)\\\\=k(q_1q_2)/((2r)^2)\\\\=k(q_1q_2)/(4r^2)\\\\=(1)/(4)* (kq_1q_2)/(r^2)\\\\F'=(F)/(4)`

So, the new force will become 1/4 times of the initial force.