Question

If the distance is halved and the charges of both particles are doubled, the force is ________ as great.

Answer 1

The new force is 16 times of the initial force.

Step-by-step explanation:

The electric force between charges is given by :

`F=(kq_1q_2)/(r^2)`

If the distance is halved, d' =d/2 and charges are doubles,
`q_1'=2q_1\ \text{and}\ q_2'=2q_2`

New force becomes,

`F'=(kq_1'q_2')/(r'^2)\\\\F'=(k(2q_1)(2q_2))/((d/2)^2)\\\\F'=16* (kq_1q_2)/(r^2)\\\\F'=16F`

So, the new force is 16 times of the initial force.