Question

Objects 1 and 2 attract each other with a electrostatic force of 18.0 units. If the charge of Object 1 is halved, then the new electrostatic force will be _____ units.

Answer 1

9.0 units

Step-by-step explanation:

The magnitude of the electrostatic force between two charged objects is given by Coulomb's law:

`F=k(q_1 q_2)/(r^2)`

where:

`k=9\cdot 10^9 Nm^(-2)C^(-2)` is the Coulomb's constant

`q_1, q_2` are the two charges of the two objects

r is the separation between the two charges

The force is:

- Attractive if the charges have opposite signs

- Repulsive if the charges have same sign

In this probleem, the initial force between the two objects is

F = 18.0 units

Then, the charge of object 1 is halved, so the new charge is

`q_1'=(q_1)/(2)`

Therefore the new force is

`F'=(kq_1' q_2)/(r^2)=(k(q_1/2)q_2)/(r^2)=(1)/(2)((kq_1 q_2)/(r^2))=(F)/(2)`

So, the force will also halve: therefore, the new force will be 9.0 units.