Answer:
3 N.
Step-by-step explanation:
If you want to know how much two charges push or pull each other, you can use Coulomb's law. It says that the force F depends on how big the charges are (Q and q) and how far apart they are (r). The bigger the charges and the closer they are, the stronger the force. The smaller the charges and the farther they are, the weaker the force. The exact formula is:
F = k | Q q | / r 2
where k is a number that makes everything work out right. It's about 8.99 × 10 9 N ⋅ m 2 / C 2 .
Now let's say you have two charges that are a certain distance r 0 apart and they have a force F 0 between them. What happens if you move them twice as far apart? The new distance is 2 r 0 and the new force is F 1 . How do F 1 and F 0 compare? Well, you can use Coulomb's law again and divide them:
F 1 / F 0 = (k | Q q | / (2 r 0 ) 2 ) / (k | Q q | / r 0 2 )
If you simplify this, you get:
F 1 / F 0 = (1/2) 2
F 1 / F 0 = 1/4
This means that the new force is only one-fourth of the old force. So if the old force was 12 N, then the new force is:
F 1 = F 0 /4
F 1 = (12 N) /4
F 1 = 3 N
So moving the charges twice as far apart makes the force four times weaker. It goes from 12 N to 3 N.